Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 1
Lecture 37 Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Physics of Technology
PHYS 1800
Lecture 37
Quantum Mechanics in a Day
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 2
Lecture 37 Slide 2
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet
*Homework Handout
PHYSICS OF TECHNOLOGY - PHYS 1800 ASSIGNMENT SHEET
Spring 2009 Date Day Lecture Chapter Homework Due Feb 16 17 18 19 20
M Tu W H F*
Presidents Day Angular Momentum (Virtual Monday) Review Test 2 Static Fluids, Pressure
No Class 8 5-8 5-8 9
-
Feb 23 25 27
M W F*
Flotation Fluids in Motion Temperature and Heat
9 9 10
6
Mar 2 4 6
M W F*
First Law of Thermodynamics Heat flow and Greenhouse Effect Climate Change
10 10 -
7
Mar 9-13 M-F Spring Break No Classes Mar 16 18 20
M W F*
Heat Engines Power and Refrigeration Electric Charge
11 11 12
8
Mar 23 25 26 27
M W H F*
Electric Fields and Electric Potential Review Test 3 Electric Circuits
12 13 9-12 13
-
Mar 30 Apr 1 3
M W F
Magnetic Force Review Electromagnets Motors and Generators
14 9-12 14
9
Apr 6 8 10
M W F*
Making Waves Sound Waves E-M Waves, Light and Color
15 15 16
10
Apr 13 15 17
M W F*
Mirrors and Reflections Refraction and Lenses Telescopes and Microscopes
17 17 17
11
Apr 20 22 24
M W F
Review Seeing Atoms The really BIG & the really small
1-17 18 (not on test) 21 (not on test)
No test week 12
May 1 F Final Exam: 09:30-11:20am * = Homework Handout
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 3
Lecture 37 Slide 3
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
Interference
Young’s Double Slit experiment
d
Dny
nnXX
n
...2,1,0,21
You must add amplitudes E, not powers P (intensities)
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 4
Lecture 37 Slide 4
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Interference of Light Waves
Is light a wave or a particle?– If it is a wave, it should exhibit interference
effects:
Recall that two waves
can interfere
constructively or
destructively depending
on their phase.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 5
Lecture 37 Slide 5
INTRODUCTION TO Modern Physics PHYX 2710
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Light from a single slit is split by passing through two slits, resulting in two light waves in phase with each other.The two waves will interfere constructively or destructively, depending on a difference in the path length.If the two waves travel equal distances to the screen, they interfere constructively and a bright spot or line is seen.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 6
Lecture 37 Slide 6
INTRODUCTION TO Modern Physics PHYX 2710
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If the distances traveled differ by half a wavelength, the two waves interfere destructively and a dark spot or line appears on the screen.If the distances traveled differ by a full wavelength, the two waves interfere constructively again resulting in another bright spot or line.The resulting interference pattern of alternating bright and dark
lines is a fringe pattern.
path difference dy
x
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 8
Lecture 37 Slide 8
INTRODUCTION TO Modern Physics PHYX 2710
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Similarly, interference can occur when light waves are reflected from the top and bottom surfaces of a soap film or oil slick.
The difference in the path length of the two waves can produce an interference pattern.
This is called thin-film interference.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 9
Lecture 37 Slide 9
INTRODUCTION TO Modern Physics PHYX 2710
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Different wavelengths of light interfere constructively or destructively as the thickness of the film varies.
This results in the many different colors seen.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 10
Lecture 37 Slide 10
INTRODUCTION TO Modern Physics PHYX 2710
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The thin film may also be air between two glass plates. Each band represents a different thickness of film.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 11
Lecture 37 Slide 11
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Diffraction and Gratings
The bright fringes in a double-slit interference pattern are not all equally bright.– They become less bright farther from the center.– They seem to fade in and out.
This effect, called diffraction, is due to interference of light coming from different parts of the same slit or opening.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 15
Lecture 37 Slide 15
INTRODUCTION TO Modern Physics PHYX 2710
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Diffraction
For constructive interference:
...2,1,0
,)sin(
n
ndDifferencePath
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 16
Lecture 37 Slide 16
INTRODUCTION TO Modern Physics PHYX 2710
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The diffraction pattern produced by a square opening has an array of bright spots.
Looking at a star or distant street light through a window screen can produce a similar diffraction pattern.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 17
Lecture 37 Slide 17
INTRODUCTION TO Modern Physics PHYX 2710
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X-Ray Diffraction
Braggs’s Law: nλ=2d sin(Θ)
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 18
Lecture 37 Slide 18
INTRODUCTION TO Modern Physics PHYX 2710
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Why study everyday phenomena?
The same physical principles that govern our everyday experiences also govern the entire universe
– A bicycle wheel, an atom, and a galaxy all operate according to laws for angular momentum.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 19
Lecture 37 Slide 19
INTRODUCTION TO Modern Physics PHYX 2710
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What are the major subfields in Physics?
Classical Physics (pre 20th century)– Mechanics → forces, motion– Thermodynamics → heat, temperature– Electricity and magnetism → charge, currents – Optics → light, lenses, telescopes
Modern Physics (20th century)– Atomic and nuclear → radioactivity, atomic power
– Quantum mechanics } → basic structure matter– Particle physics– Condensed matter → solids and liquids, computers,
lasers– Relativity, Cosmology → universe, life!
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 20
Lecture 37 Slide 20
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
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State of Physics cira 1895
Electricity & MagnetismMaxwell Equations (c 1880)• Gauss’ Law•Faraday’s Law•Ampere’s Law•No magnetic monopoles
Mechanics (Gravity) Newton’s Laws (c 1640)1-Law of inertia2-F=ma3-Equal and opposite reactions
Conservation Laws• Energy• Linear & Angular Momentum
Statistical Mechanics• 3 Laws of Thermodynamics• Kinetic Theory
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 21
Lecture 37 Slide 21
INTRODUCTION TO Modern Physics PHYX 2710
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Limits of pre-Modern Physics
Dimension Range of Applicability
Range of Application
Length 10-6 to 10+8 m Smoke particle (Brownian Motion) to the solar system
Mass 10-9 to 10+31 kg Dust particles to solar mass
Time 10+10 to 10+17 sec-1
10-3 to 10+9 sec
Microwave to UV light
Smallest timing increments (msec) to celestial motions (centuries)
Velocity 10-6 to 10+5 m/s Small particles to celestial motion
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 22
Lecture 37 Slide 22
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
Then All Hell Broke Lose“Thirty Years That Shook Physics”
• 1887 Michelson-Morley exp. debunks “ether” • 1895 Rontgen discovers x rays• 1897 Becquerel discovers radioactivity• 1897 Thomson discovers the electron• 1900 Planck proposes energy quantization• 1905 Einstein proposes special relativity• 1915 Einstein proposes general relativity• 1911 Rutherford discovers the nucleus• 1911 Braggs and von Laue use x rays to determine crystal structures• 1911 Ones finds superconductors• 1913 Bohr uses QM to explain hydrogen spectrum• 1923 Compton demonstrates particle nature of light• 1923 de Broglie proposes matter waves• 1925 Davisson & Germer prove matter is wavelike• 1925 Heisenberg states uncertainty principle• 1926 Schrodinger develops wave equation• 1924-6 Boson and Fermion distributions developed
• 1949 Murphy's Law stated
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 23
Lecture 37 Slide 23
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
Current State of Physics cira 2009
Electricity & MagnetismMaxwell Equations (c 1880)
Weak Nuclear Force Radioactivity
Strong Nuclear ForceComposition of subatomic particles
Mechanics (Gravity)…… General RelativitySpace and time
Standard Model • QCD• Unites E&M, Strong NF, Weak NF
Conservation Laws• Energy• Linear & Angular Momentum• Charge, Spin• Lepton and Baryon Number
Quantum Mechanics•Schrodinger/Dirac Equation•Probabilistic approach
Statistical Mechanics• Physics of many particles• Fermions and Bosons• Partitioning of Energy• Thermodynamics• Time and Entropy
Weinburg-Salom Model• QED• Unites E&M, Weak NF
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 24
Lecture 37 Slide 24
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Limits of Current Modern Physics
Dimension Range of Applicability
Range of Application
Length 10-18 to 10+26 m Quark size to the universe size
Mass 10-31 to 10+40 kg Electrons to galactic clusters
Time 10+3 to 10+22 sec-1
10-16 to 10+17 sec
Radio to Gamma rays
Sub-femtosecond spectroscopy to age of universe
Velocity 10-8 to 10+8 m/s Sub-atomic particles to speed of light
Quantum Mechanics
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Lecture 37 Slide 25
INTRODUCTION TO Modern Physics PHYX 2710
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Cathode rays, Electrons, and X-rays
By the end of the nineteenth century, chemists were using the concept of atoms to explain their properties.
Physicists were less convinced.– The discovery of cathode rays was the beginning of
atomic physics.Two electrodes are sealed in a glass tube.
As the tube is evacuated, a glow discharge appears in the gas between the electrodes.
With further evacuation, the discharge disappears, and a glow appears on the end of the tube opposite the cathode.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 26
Lecture 37 Slide 26
INTRODUCTION TO Modern Physics PHYX 2710
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An invisible radiation seemed to emanate from the cathode to produce the glow on the opposite wall of the tube.– The invisible radiation was called cathode rays.
If the north pole of a magnet is brought down toward the top of a cathode-ray tube, the spot of light is deflected to the left across the face of the tube.– This indicates the cathode rays are negatively
charged particles.Two electrodes are sealed in a glass tube.
As the tube is evacuated, a glow discharge appears in the gas between the electrodes.
With further evacuation, the discharge disappears, and a glow appears on the end of the tube opposite the cathode.
Quantum Mechanics
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J. J. Thomson used both electric fields and magnetic fields to deflect the beam.
The combined effect allowed him to estimate the velocity of the particles.
With the deflection produced by the magnetic field alone, this allowed him to estimate the mass of the particles.
– We now call these particles electrons.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 28
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INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
You probably use cathode rays almost every day.
The heart of most television sets is the cathode ray tube, or CRT.
Do you know how a TV works?
Quantum Mechanics
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Lecture 37 Slide 29
INTRODUCTION TO Modern Physics PHYX 2710
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The electrodes that produce and focus the electron beam are called the electron gun.
– An electric current passes through the filament to heat the cathode to emit electrons.
– Electrons are accelerated from the cathode to the anode by the high voltage.
– Electrons passing through the hole in the anode make up the electron beam.
After leaving the electron gun, the beam of electrons travel across the tube, producing a bright spot of light when it strikes the glass face of the tube.
Magnets deflect the beam so that it strikes different points on the face of the tube at different times.
The beam scans across the entire face of the tube in a fraction of a second, to form the picture.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 30
Lecture 37 Slide 30
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
Experiments on the “New”Particle”The Electron
Robert Millikan measured the quantized charge on the electron J.J. Thomson measured the
charge-to-mass ratio e/m
Quantum Mechanics
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Lecture 37 Slide 31
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
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Davisson and Germer Experiment
In 1927 Davisson and Germer first demonstrated the diffraction patterns generated by electrons of 10eV passing through a Ni crystal.
nmeVmE
h 226.1
2
For electrons:
Quantum Mechanics
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Lecture 37 Slide 32
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
Electron Diffraction
Energy Electron Diffraction: Electron and x-ray both exhibit diffraction from crystals.
Braggs’s Law: nλ=2d sin(Θ)
Quantum Mechanics
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Lecture 37 Slide 33
INTRODUCTION TO Modern Physics PHYX 2710
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Electron Interference Electron Single Slit Interference: Effects are clearly observed. However, as soon as “electron tracking” is instituted, the interference pattern disappears!
Quantum Mechanics
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Lecture 37 Slide 34
INTRODUCTION TO Modern Physics PHYX 2710
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Low Energy Electron Diffraction
Low Energy Electron Diffraction is a standard tool in surface science. ~50 eV electrons with λ~1 Å are diffracted from surface atoms to determine atomic structure.
Typical LEED systems. (left) UHV surface analysis chamber. (right) LEED electron guns and grids.
Quantum Mechanics
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Lecture 37 Slide 35
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
LEED Images
A SPA LEED image of silicon taken with 128 eV electrons.
The organic molecule PTCDI adsorbed on the 110 surface of Ag.
Quantum Mechanics
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Lecture 37 Slide 36
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Neutron Diffraction
(left) Triple axis neutron diffractometer at the NIST Neutron scattering facility. (right) Diffraction pattern from nuetrons.
Quantum Mechanics
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INTRODUCTION TO Modern Physics PHYX 2710
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...even ...even Quantum Quantum Physics Physics (matter (matter waves)...waves)...
Quantum Mechanics
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INTRODUCTION TO Modern Physics PHYX 2710
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Nobel Prizes Related to Wave-Particle Duality
There have been 14 Nobel Prizes in physics awarded that have some direct relation to the wave-particle duality. Albert Einstein received the Nobel Prize for one of these, the photoelectric effect.
Annotated list of winners.
Quantum Mechanics
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INTRODUCTION TO Modern Physics PHYX 2710
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Pioneers in the Wave Theory of Particles
Born Heisenburg Schrodinger
Quantum Mechanics
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Lecture 37 Slide 40
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Particles as a Wave
In 1924 de Broglie suggested that electrons may have wave properties. The wave length of an electron is proposed to be h/p where p is the momentum of the electron.
• This expression is consistent with photon (E=pc) or p=h/ λ.
• Because of the Planck constant, the λ of macroscopic object is not detectable.
• Lower momentum particle is more wavelike.
• Higher energy wave is more particle like.
mv
h
p
h
p
h
particlephoton
nmEmE
h 226.1
2
De Broglie waves:
For electrons:
Quantum Mechanics
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INTRODUCTION TO Modern Physics PHYX 2710
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De Broglie Wave Problems
What is the de Broglie wave length of a Germer electron?
What is the de wave length of a jelly bean?
Assume the mass of the jelly bean is 5 g and its velocity is 1 m/s. The total energy is just the kinetic energy E=KE=1/2 mv2 .
Then
!106 32 mph And
eVJm
pE 162
2106101
2
For an electron all the electrostatic PE is converted to KE, eV 1/2 mv2 . First solve for p then for λ.
First
!106 10 mph
Then
eVJm
peVE 50108
218
2
Quantum Mechanics
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Waves of what?
The physical interpretation of de Broglie waves (the wave function or Schrodinger waves) is related to the probability of finding a moving particle at a particular location (x,y,z) and time t.
• Because Ψ(x,y,z,t) is complex and can be positive or negative, it cannot be the probability directly.
• | Ψ(x,y,z,t) |2 is the probabilityof finding the particle at location (x,y,z) at time t.
• To be a probability function, it must obey a normalization condition stating it must be somewhere:
1),,(2 dVzyx
Born
Schrodinger
Quantum Mechanics
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Lecture 37 Slide 43
INTRODUCTION TO Modern Physics PHYX 2710
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The Schrödinger Equation
t
txitxxU
x
tx
m
,
,)(,
2 2
22
:),( tx
2),( txP probability to find the particle at (x,t)
normalization of the wave function
must be continuous),,( tx ,),(
x
tx
,),(
t
tx
Complex wave function
1)(),(22
dxxdxtx
Time independent Schrödinger equation xExxUdx
xd
m
)(2 2
22
Let tiextx )(),( xxxU
dx
xd
m
)(2 2
22
U(x): Potential Energy
The SchrodingerWave equation:
Quantum Mechanics
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INTRODUCTION TO Modern Physics PHYX 2710
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Matter is made up of atoms…
The Atomic Theory, a cornerstone of modern science, was proposed by an early Greek thinker, Democritus (c.460 BC - c.370 BC).
2400 year later, Feynman deemed this the most important notion in science
Quantum Mechanics
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Trying to see atoms…
Optical image
(5 X mag)
SEM Image
(300,000 X mag)
STM Image
(3,000,000 X mag)
STM Image
(24,000,000 mag)
Magnified images of semiconductor chip.
Quantum Mechanics
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INTRODUCTION TO Modern Physics PHYX 2710
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Seeing atoms…finally!!!
Atomic scale images seen with scanning tunneling microscope
STM developed in 1985 at IBM
Measures extent of electron cloud
Binnig and Roher’s original STM
Quantum Mechanics
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Examples of STM images…
Pt (100) with vaccancies
Si (111) 7x7 reconstruction
Annealed decanethiol film on Au(111)
Si (111) with terraces and vaccancies
Quantum Mechanics
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Examples of STM images (part 2)…
Quantum Mechanics
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Barrier Penetration (QuantumTunneling)
The thicker or higher the barrier, the less the tunneling probability approaches classical result
There is a certain probability T that the particle can tunnel through the barrier,
kadxxkeeT
a
2)(20
ExVm
k
)(2
where
V0
x
E
a
V(x)
0
otherwise
axVxV o
,0
0,)(
Ψ is damped
Ψ oscillates
Quantum Mechanics
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How an STM works…
• An STM s a glorified phonograph needle
• Tip motion uses piezioelectric crystals
• Tunneling current results from overlap of electron wavefunction with conducting surface
Quantum Mechanics
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How an STM works (part 2)…
Quantum Mechanics
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Corralling electrons…
STM used to make direct maps of the Quantum Mechanicsl probability distribution of the electron wave function of 2D state confined by “corrals” made of adsorbed atoms.
Quantum Mechanics
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Physics of Technology—PHYS 1800
Spring 2009
Corralling electrons…
STM used to make direct maps of the Quantum Mechanicsl probability distribution of the electron wave function of 2D state confined by “corrals” made of adsorbed atoms.
Quantum Mechanics
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Physics of Technology—PHYS 1800
Spring 2009
Corralling electrons…
STM used to make direct maps of the Quantum Mechanicsl probability distribution of the electron wave function of 2D state confined by “corrals” made of adsorbed atoms.
Quantum Mechanics
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Lecture 37 Slide 55
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
Corralling electrons…
STM used to make direct maps of the Quantum Mechanicsl probability distribution of the electron wave function of 2D state confined by “corrals” made of adsorbed atoms.
Quantum Mechanics
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Applications of knowledge on the atomic scale…
Feynman: “Plenty of room at the bottom”
– Inevitability of small– Interface of
quantum mechanics with applications
Quantum Mechanics
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Moving atoms one layer at a time…
Molecular Beam Epitaxy
Quantum Mechanics
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Moving atoms one at a time…
Quantum Mechanics
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Moving atoms one at a time…
Quantum Mechanics
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Engineering Nanomachines
Quantum Mechanics
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Designer Molecules
Quantum Mechanics
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Moving many atoms
Shen’s worSTM images of the H-terminated Si(100) surfaces
3 x 1 Monohydride + Dihydride
2 x 1 Monohydride
1x1 Dihydride
H
Si
200Åx200Å
Electron stimulated H/D-desorption from Si(100)-2x1 surface
USU Nanolithography
Lab
TC Shen
Quantum Mechanics
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Here at USU, TC Shen can make wires 1 atom wide!
An atom is ~0.1 nm across.The moon is 4x108 m from the Earth (see front cover).
How many atoms, in a 1 atom wide wire, would it take to reach the Moon?
How much would this amount of Cu weigh?
Quantum Mechanics
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Atomic scale electronicsSingle electron transistor
Chips ot the quantum scale
Transistors on a chip that switch with a single electron
Quantum Mechanics
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Quantum Computing
Macro to Micro
Micro to Nano
Nano to Sub-nano
Quantum Mechanics
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Watching stuff happen…
Chemistry time scales
STM
Femtosecond probes
Quantum Mechanics
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Femtosecond spectroscopy at USU…
USU Femtosecond Spectroscopy Lab
D. Mark Riffe
Probing dynamics of hot electrons
Quantum Mechanics
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What We Know About Atoms
Nucleus
Chemical properties are determined by electron configurations.
e
Atoms are electrically neutral
1 fm=10-15 m
protons+ neutrons
p, n
1-10 fermi (fm)
Atomic number (Z)= number of protons
Atom 0.1 nm= 1Å 1 Å=10-10 m
Z= number of electrons
Chemically inert : completely filled outer shells
Chemically active : single e (alkali) or vacancy (halogene) in the outer shell
Ion : atom lost or gained one or more electrons
Valence electrons : electrons in the outer shell
Quantum Mechanics
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Structural Models of the Atom
2
200 02ar r
Ze
e
Thomson “Plumb Pudding” Model
Bohr “Planetary” Model QM “Probability” Model
Rutherford “Point Nucleus” Model
Aristotle’s “Point” Model
Quantum Mechanics
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The Uncertainty Principle
and
Werner Heisenberg
Uncertainty Principle 1927
Nobel Prize 1932
It can be shown that the minimum of the product of the two conjugate observables is 2
2 px 2 tE
Usually the uncertainty product is much greater than 2
If an excited energy of an atom has a lifetime τ, its energy cannot be known better than 2
Accuracy of the position measurements depends on wavelength.Smaller wavelength means more momentum.No observation will not disturb the subject.
If a particle is confined in a space of length L, Lp 2
The kinetic energy of the particle must be greater than a minimum,
2
22
82 mLm
p Zero-point energy
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 72
Lecture 37 Slide 72
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Physics of Technology—PHYS 1800
Spring 2009
The Uncertainty Principle
Changes in momentum imparted by photon:
Uncertainty in position determined by photon probe wavelength:
hp x
hxp
Quantum Mechanics
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Lecture 37 Slide 73
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Spring 2009
Atomic Spectra
Atomic Emission Spectrophotometer
Atomic Emission Spectrum of Hydrogen
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 74
Lecture 37 Slide 74
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Spring 2009
The First Excited States Wave Functions of H-atom
1st excited state has three degenerated states
02
23
0200200 2 aZre
a
ZrC
n=2, l=0, m=0
n=2, l=1, m=±1
cos02
0210210
aZrea
ZrC n=2, l=1, m=0
iaZr eea
ZrC
sin02
0211121
2
200 02ar
2
2112
210
rp
0ar2 4 6
22
210 r 22
200 r
Bohr model:Z
anr 02
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 75
Lecture 37 Slide 75
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Physics of Technology—PHYS 1800
Spring 2009
Probability Distributions for Hydrogen Atom
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 76
Lecture 37 Slide 76
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Physics of Technology—PHYS 1800
Spring 2009
Periodic Table
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 77
Lecture 37 Slide 77
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Formation of Bands in Solids
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 78
Lecture 37 Slide 78
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
An integrated circuit consists of several transistors, diodes, resistors, and electrical connections all built into a single tiny chip of semiconductor material, usually silicon.– This allows the production of circuits much smaller than circuits
made from individual transistors or vacuum tubes.– A computer that would fill a large room can now be reduced to the
size of a hand-held calculator.
The starting point in producing integrated circuits is a polished wafer of single-crystal silicon.Several identical circuits are usually imprinted on a single silicon wafer.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 79
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– The wafer is cut into individual chips, each containing a miniature circuit.– The final steps involve making electrical connections to the chip, packaging the
chip in a sealed plastic enclosure, and testing the resulting circuit.
Quantum Mechanics
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– Rows of packaged microchips are used on a single circuit board of a computer.– Competition to produce ever smaller and faster circuitry continues to push the
technology forward.
Research in the condensed-matter physics of semiconducting elements and compounds has become one of the most active areas in modern physics.The revolution in electronics technology is still proceeding.
Quantum Mechanics
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Lecture 37 Slide 81
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Physics of Technology—PHYS 1800
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Superconductors and Other New Materials
Superconductivity is a phenomenon in which the resistance to the flow of electric current completely disappears.
The resistance of many metals drops abruptly to zero at the critical temperature Tc.An electric current, once started, would flow indefinitely with no source of power.
Quantum Mechanics
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Lecture 37 Slide 82
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The Meissner Effect
One striking property of a superconductor is that it will completely exclude magnetic field lines produced by an external magnet or electrical current.
A magnet brought near a superconducting material will be repelled.A small magnet can levitate above a superconducting disk cooled with liquid nitrogen.
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 83
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Physics of Technology
Next Recitation: Math and Problem Solving Review
Tuesday 1:30-2:45
ESLC 53
Review Appendices A,B,C
Next Class: Wed 10:30-11:20
BUS 318 room.
Quantum Mechanics
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Inconsistencies in Physics cira 2009
Electricity & MagnetismMaxwell Equations (c1880)
Weak Nuclear Force • Radioactivity
• CPT violations?
Strong Nuclear Force•Composition of subatomic particles•Matter/anitmatter imbalance•Decay ratios and particle masses•Search for Higgs Bosons•Nature of strong hadron force•Proton decay
Gravity……………… • General Relativity• Space and time• Inconsistent with QM• Search for dark matter• Fixed gravitational constant?
GUT’s and TOE’s • Combining Standard model and Gravity• String Theory
Heavy Fermions and HTSC
Conservation Laws• Energy• Linear & Angular Momentum• Charge, Spin• Lepton and Baryon Number
Quantum Mechanics• Existence of atoms•Schrodinger/Dirac Equation• Sub-atomic particles• Probabilistic approach•Teleportation•Entwined states•Sub-Planck length physics
Statistical Mechanics• Fermions, Bosons and Anyons•Bose-Einstein Condensates•Superconductivity•Stellar Evolution• SM of Black Holes• Time and Entropy
Chaotic and complex systems
Quantum Mechanics
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The forces in the universe have also been grouped into a few fundamental forces:– The primary force responsible for binding the quarks in
neutrons, protons, and other baryons and mesons is the strong nuclear interaction.
– The weak nuclear force is involved in the interactions of leptons, such as beta decay.
– The electric force and magnetic force have been combined into the electromagnetic force.
Quantum Mechanics
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– The standard model has now unified the electromagnetic force with the weak nuclear force to form the electroweak force.
– A Grand unified theory (GUT) which will unify the strong force with the electroweak force is much sought after.
– This leaves only the gravitational force.– A Theory of everything (TOE) may someday unify all
forces, including gravity.
Quantum Mechanics
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Have you ever seen an atom?
Why do we think atoms exist?
Do you believe in atoms?
Quantum Mechanics
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Radioactivity and the Discovery of the NucleusWhen Becquerel placed a piece of phosphorescent material
on a covered photographic plate, the developed plate showed a silhouette of the sample.
Radiation apparently was passing from these materials to expose the film.
Quantum Mechanics
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The basic building blocks of the nucleus are the proton and the neutron.– Their masses are nearly equal.– The proton has a charge of +1e while the neutron is
electrically neutral.
This explains both the charge and the mass of the nucleus.– An alpha particle with charge +2e and mass 4 x mass of the
proton is composed of two protons and two neutrons.– A nitrogen nucleus with a mass 14 times the mass of a
hydrogen nucleus and a charge 7 times that of hydrogen is composed of seven protons and seven neutrons.
Quantum Mechanics
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Lecture 37 Slide 90
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Quantum Mechanics
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Radioactive Decay
Becquerel discovered natural radioactivity in 1896.By 1910, Rutherford and others demonstrated that
one element was actually being changed into another during radioactive decay.
The nucleus of the atom itself is modified when a decay occurs.– For example, Marie and Pierre Curie isolated the highly
radioactive element radium which emitted primarily alpha particles.
Quantum Mechanics
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Nuclear Reactions and Nuclear Fission
In addition to spontaneous radioactive decays, changes in the nucleus may be produced experimentally through nuclear reactions.
Quantum Mechanics
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Spring 2009
Nuclear Reactors
Fermi’s strategy to achieve a chain reaction with natural or slightly enriched uranium:– Slow the neutrons down between fission reactions using a
material called a moderator.– Control rods are used to absorb the neutrons to slow the
reaction as desired.
Fermi’s “pile” was the first human-produced nuclear reactor.Graphite blocks served as the moderator.Control rods were cadmium, but today’s reactors use boron.
Quantum Mechanics
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Modern Power Reactors
Most reactors today use ordinary (light) water as the moderator.This requires enrichment of the fuel to 3% U-235.The advantage is that the water can also be used as a coolant.
Quantum Mechanics
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A hydrogen bomb involves nuclear fusion rather than fission.– Nuclear fusion is another kind of nuclear reaction that also
releases large quantities of energy.– Fusion is the energy source of the sun and other stars as well as
of thermonuclear bombs.– In a sense, it is the opposite of fission: very small nuclei such as
hydrogen, helium, and lithium combine to form larger nuclei.– As long as the mass of the reaction products is less than the
mass of the original isotopes, energy is released.
One possible reaction is the combination of two isotopes of hydrogen, deuterium and tritium, to form helium-4 plus a neutron:
Quantum Mechanics
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Can we generate power from controlled fusion?
Producing fusion reactions for a commercial power source has not yet been accomplished.– Confining the fuel at very high temperatures in a very small space
presents extreme difficulties.
Experimental reactors such as the Tokamak Fusion Test Reactor at Princeton, NJ, have generated energy from fusion, but they have not reached the break-even point, where as much energy is released as is required to initiate the reaction.Research on this problem may someday reach that goal.
Quantum Mechanics
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Quarks and Other Elementary Particles
Atoms were once thought to be the basic building blocks of all matter.
We now know atoms consist of electrons, protons, and neutrons.
Neutrons and protons also have a substructure of quarks.
Quantum Mechanics
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Where will this all end?
What are quarks and why do we believe they exist?Will we someday discover that quarks also have a
substructure?Recent advances in high-energy physics have produced the
standard model.
Particle accelerators like CERN in Europe and Fermilab in the U.S. are used to bombard targets with fast-moving particles.Particle detectors are used to study what emerges from these collisions.For example, particle tracks in a bubble chamber provide information on the new particles produced in collisions or decays.
Quantum Mechanics
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How was the
universe formed?How is it
changing?
... to the largest.
Quantum Mechanics
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The Michelson-Morley Experiment
Michelson and Morley used an interferometer to detect small differences in the velocity of light or in the distance that the light traveled.
Light waves traveling along the two perpendicular arms interfere to form a pattern of light and dark fringes.
Quantum Mechanics
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The Michelson-Morley Experiment
At some time during the year the earth should be moving relative to the ether.
No fringe shift was observed; the experiment failed to detect any motion of the earth relative to the ether.
This “failure” was a very important result!
Quantum Mechanics
Introduction Section 0 Lecture 1 Slide 109
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Einstein’s Postulates of Special Relativity
Einstein’s solution to the dilemma of the ether and the speed of light was both simple and radical.– Postulate 1: The laws of physics are the same in any
inertial frame of reference.
– Postulate 2: The speed of light in a vacuum is the same in any inertial frame of reference, regardless of the relative motion of the source and observer.
The first is just a reaffirmation of the principle of relativity stated earlier.
The second is much more radical: light does not behave like most waves or moving objects.
Quantum Mechanics
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Newton’s Laws and Mass-Energy Equivalence
Accepting Einstein’s postulates requires some major changes in how we think about space and time.
For example, does Newton’s second law of motion still apply when objects are moving at large velocities?
F = ma = p / tIn order to maintain conservation of momentum,
Einstein redefined momentum asp = mv
Quantum Mechanics
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Lecture 37 Slide 111
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General Relativity
What happens if our frame of reference is accelerating?
Imagine that we are in a moving elevator, for example.
If the elevator is moving with constant velocity, no experiment that we can do inside the elevator could establish whether or not we are moving.If the elevator is accelerating, a bathroom scale would register a greater weight.
Quantum Mechanics
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Similarly, space is curved near a very strong gravitational field.
– This represents how things might be pulled into the center of the field.
– Since light rays are bent by strong gravitational fields, they can be pulled into the center of the field as well as particles having some mass.
Quantum Mechanics
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This figure is a two-dimensional representation of a black hole.
– Black holes are thought to be very massive collapsed stars, which generate an extremely strong gravitational field.
– Space is very curved in their vicinity.
Quantum Mechanics
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Einstein’s theories of special and general relativity have had an enormous impact on our concepts of space and time.
Special relativity deals with reference frames that, although moving at speeds near the speed of light, are still inertial (non-accelerating).
General relativity deals with accelerated reference frames.
The predictions of these theories have been well confirmed.– For example, the energy released in nuclear reactions is a result of
mass-energy equivalence.– Also, astronomical observations of the bending of starlight is evidence of
the principle of equivalence between gravity and acceleration.
These ideas excite the imagination and are still very active areas of research.
Quantum Mechanics
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Cosmology and the Beginning of Time
We have now looked into the extremely small:– Quarks make up protons and neutrons, which form the nucleus.– Atoms consist of the nucleus and the surrounding electrons.– Atoms make up molecules and the ordinary matter of our world.
What about the very large?– The earth is part of the solar system which includes the sun.– The sun is just one star in our galaxy, which is just one galaxy in
our Local Group of galaxies.– These groups of galaxies make up larger groups, and ultimately,
the universe.
What can our knowledge of atoms, nuclei, and quarks tell us about the universe?
Quantum Mechanics
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Hurtzsprung-Russell (H-R) Diagram
4ML MTe
1R
0.01R
1000R
Sun
Sirius A
Sirius B
Polaris
Betelgeuse
Arcturus
Antares
100R
