7/27/2019 Quantum Ideas Notes Week 1
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Quantum Ideas
Syllabus:
The success of classical physics, measurements in classical physics. The nature of light,the ultraviolet catastrophe, the photoelectric effect and the quantisation of radiation. Atomicspectral lines and the discrete energy levels of electrons in atoms, the Frank-Hertz ex-periment and the Bohr model of an atom.
Magnetic dipoles in homogeneous and inhomogeneous magnetic fields and the Stern-Gerlach experiment showing the quantisation of the magnetic moment. The Uncertaintyprinciple by considering a microscope and the momentum of photons, zero point energy,stability and size of atoms. Measurements in quantum physics, the impossibility of measur-ing two orthogonal components of magnetic moments. The EPR paradox, entanglement,hidden variables, non-locality and Aspect's experiment, quantum cryptography and theBB84 protocol. Schrdinger's cat and the many-world interpretation of quantum mechan-ics. Interferometry with atoms and large molecules. Amplitudes, phases and wavefunc-tions. Interference of atomic beams, discussion of two-slit interference, Bragg diffraction ofatoms, quantum eraser experiments. A glimpse of quantum engineering and quantumcomputing. Schrdinger's equation and boundary conditions. Solution for a particle in an
infinite potential well, to obtain discrete energy levels and wavefunctions.
Quantum Ideas 2007 Axel Kuhn
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Quantum
Physics
Failureof
ClassicalPhysics
Photoelectric
Effect
Blackbody
Radiation
Uncertainty
Principle
Plancks
Hypothesis
W
ave-Particle
D
uality
Paradoxainearly
Gedanken-experiments
Entanglement
Superposition
Probabilities
Roleoftheobserver
Break-downof
the
Wavefunction
Many-worldinterpretation
ModernApplications
Quantum
Cryptography
Quantum
Computing
Stru
ctureofMatter
Ato
mmodel(Bohr)
Molecules,Solidstate,etc.
Schrdingers
Equation
Interferenceof
massiveparticles
Quantised
energylevels
Q
uantisation
o
fradiation
DeBrogie
Wavelength
Spectrallines
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Classical Physics:
classical mechanics (Newton; F = m a)
electricity and magnetism (Coulomb, Faraday, Maxwell)
electromagnetic waves (rf ... light ... x-ray ... gamma)
thermodynamics (energy conservation, equilibration, statistical mechanics)
accurate measurement of all observables (position x(t)and momentum p(t) )
Quantum Physics:
probabilistic - not deterministic (Einstein: Good does not play dice)
probability wave function (x,t) to describe a particle
superposition and entanglement
non-local behaviour (Spooky interaction at a distance that bothered Einstein)
uncertainty principle: x p /2 and E t /2
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Quantum Ideas 2007 Axel Kuhn
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Quantum Ideas 2007 Axel Kuhn
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Quantum Ideas 2007 Axel Kuhn
7/27/2019 Quantum Ideas Notes Week 1
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illumination with a mercury lamp, filtering a single spectral line.
Cathode metal with a binding energy (or work function) of Ebind = 2.02 eV
yellow, 578nm, 5.19E+14 Hz, Ekin = 0.13 eV
green, 546nm, 5.50E+14 Hz, Ekin = 0.27 eV
blue, 436nm, 6.88E+14 Hz, Ekin = 0.81 eV
violet, 405nm, 7.41E+14 Hz, Ekin = 1.02 eV
Plancks constant is obtained from the slope of the kinetic energy, Ekin()
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Quantum Ideas 2007 Axel Kuhn
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Hints for quantisation:
a) threshold (minimum frequency required):
resonance phenomenon quantised medium or light
b) linear in the intensity (for =const).
electron number proportional to photon number
c) photo current insensitive to (provided h > Ebind)
no change of the electron current if photon flux constant albeit the intensity is increasing: Iphoto
d) no delay direct evidence!
it lasts seconds until a single atom accumulates enough energy, so the radiation cannot be continuous
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Quantum Ideas 2007 Axel Kuhn
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Quantum Ideas 2007 Axel Kuhn
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Quantum Ideas 2007 Axel Kuhn
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Blackbody = Cavity?
- Multiple reflections -> absorption of incident light
- Thermal equilibrium -> Walls Cavity modes
- Spectral energy density ()d
R()d (Radiance through whole)
- Boundary conditions: Nodes on the walls
- Standing waves along x,y,z
Consider a 2D problem and decompose into
x = / cos() y = / sin()
with nxx = 2L etc... ==> nx = (2L/) cos() and ny = (2L/) sin()
square and add these conditions (generalise into 3D):
(2L/)2 = nx2 + ny2 + nz2
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Number of Modes in the cavity with frequencies smaller than :
- sphere of radius R =(nx2 + ny2 + nz2) = 2L/ = 2L/c - mode number N() = 4/3R3 2/8 = ...
- same for N(+d) = ...
Mode number in the interval ...+d
N = N(+d) - N() = 82 L3 / c3 d
Spectral density per unit volume
()d = /L3 = 82 / c3 d
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1/t*1.* "{&ZD Lutb- *,id7
\"= )'/-x\7 =Vi*xLou- ,
L#
L
f-)r,.n-L h n-,"l lL fzL '- tL ,*tt
h" \, - ZLI h,o', ), --zLI h)r''rt = *"
7L.,\
ZLJ.qL;LJ
-' hr' *
-D 6 Lo f*,*C'J l" 3? ,
R
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Sil*'L i. lL h - slpaa svJ;u, IZ ,
//,-Lu o( ,--L = l,/o/,* ,l lL 70.,81,'hor==\rll (fry..))= ( ts' 7'trLt .r3o3L64I
8try" t,= a.'dytiJ',t=
r?,t# ,l --,,Ln
6N 0t)do=
(ot:l:.t ryn{r.^+7'.,{u*( 9.-.9, Jrt
,({,t,Ju1-//u)#'(y')'-'=8o4u1,
v 3Y'Jt'+ "(*L fu u--:L e'sb*,-I
Z g'l.,-:,J'-'
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Quantum Ideas 2007 Axel Kuhn
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Blackbody Radiation
Average energy per frequency mode, using the Boltzmann distribution P(E)
E =
En P(E)n=0
P(E)n=0
=
h ne
nhkT
n=0
enh
kT
n=0
= h
A
B
with B Bexp hkT( ) = 1
and A Aexp h kT( )= Bexp h kT( )
A
B=
1
exp hkT( ) 1
and E =h
exp hkT( ) 1
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Plancks law
Spectral energy density (energy per unit volume in the frequency range...+d):
()d=82
c3
h
exp hkT( ) 1
=8h3
c3
1
exp hkT( ) 1
total energy density:
= ()d= 85
k
4
15(hc)3 T
4= T4
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Quantum Ideas 2007 Axel Kuhn
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Quantum Ideas 2007 Axel Kuhn
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Ao^*'l a,- ola q- Pt L-= h?^tt^J/ c = hg
E;-,h,- ! = ,,o' PctIIl-]o' \
= t*t ClL(*" ( s tttt
De--Lnjt. ,"*(*rlL\ =%'7*" I iI.,"),o,ouin",u\"::f_ ?],+k tuL/...*Lo[u,*,eJ L k",J,
14'"'r'*iltLt=?x-t glno u).t/.' i
(G,t) = uflz(w-ailIv;lLa. ?rt)
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Quantum Ideas 2007 Axel Kuhn
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s&t?ro {_r"/-D d,.rk.- trLL* tJ,l-tU" +-J"{'-.6'ao'.gh|-, - "/.J** to.(-7;C.'->un-hn*"A!Jp-
u:lLL"l-- rt "kn
[n}ux{ut-
?os;"q?.*6 Ar 'I
of =r^P,9^l
CO',otte*{i*
)'s;"o(tL-%*o\t.7, 2fi,*'a
J*,J*r /Y
s Zh(t.*re)
z c)"(aL' er -
n*T fair,'tq,.t.k,a-[=hf,=b= blt\t?^'=":h.-zutLc'< t I e^: ^1
1i1t'+ 'aLn
.* (I{- ,)2,o"L i-*)- rt^*a
Quantum Ideas 2007 Axel Kuhn
7/27/2019 Quantum Ideas Notes Week 1
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I rrr '^ Vqu!/(e.-C(l"^:J
\ / t= Ao L l-a-e), . ' tt . . . r14v"rolo-lQ Ao- 7"., / _ _-,ov
c9
a-/F0/t>' I
- t2= Z.?3 - t0'- nelq
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Quantum Ideas 2007 Axel Kuhn
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Hanbury-Brown and Twiss:
Intensity correlation measurements
- dead time of the detectors
- beam splitter
- pair of photon counters
- cross correlation
Single-photon emitters:
- single atoms or ions
- crystal defects (Quantum dots)
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