PHYSICS DEPARTMENT

Introduction To Quantum

Mechanic

s

QUANTUM?

Quantum mechanics is the study of processes which occur at the atomic scale.

The word "quantum" is derived From Latin which means BUNDLE.

Therefore, we are studying the motion of objects that come in small bundles called quanta. These tiny bundles that we are referring to are electrons traveling around the nucleus.

OVERVIEW

Quantum mechanics provides in the theoretical framework which describes, with reasonably good accuracy, the behaviour of radiation and matter at atomic and subatomic levels.

It is like a revolution that has changed the old concepts of reality in many respects.

CLASSICAL VIEW

• Our universe consists of two types of entities- matter and radiation.

• Matter is made up of localised particles. The classical mechanics formulated by Newton

and further developed by Hamilton, Lagrange and many others successfully explained the motion of material particles subject to various types of forces.

Maxwell developed the electromagnetic theory in 1855 which combined electricity, magnetism and optics into a single

framework. He showed that all radiations including light are electromagnetic waves. The existence of such wave was

confirmed experimentally by hertz in 1887.

RADIATION

QUANTUM VIEW

while studying the microscopic structure of matter, the nature of e.m radiation and interaction of radiation with matter, a number of experimental results were found which could not be explained on the basis of classical mechanics.

Some of them are- • The particle nature of radiation.• The wave nature of matter. • The quantization of physical quantities.

ORIGIN OF QUANTUM MECHANICS

The originator of the quantum idea was a German physicist Max Planck.

He introduced the concept of quantisation of radiant energy in 1900 for explaining the spectral distribution of radiant energy emitted by a heated black body. Max Planck

(1858-1947)

Albert Einstein (1879-1955)

Einstein was the next, who used Plank’s idea in 1905, for explaining the puzzling features of photoelectric effect. He explained Photoelectric effect by postulating that light or more generally all e.m radiations, can be divided into finite number of "energy quanta" that are localised points in space.

Arthur Compton(1892-1962)

In 1925, Compton explained the change of wave length of X-rays when they were scattered by free weakly bound electrons (Compton effect). The findings of Einstein and Compton showed that radiation can behave as particles, thus bringing in wave-particle duality of radiation.

Prince Louis de Broglie(1892-1987)

L.de-Broglie in 1923 suggested that like radiation, matter has dual nature. This wave-particle duality of matter led to very important principle, called the Uncertainty principle discovered by Heisenberg in 1927.

Niels Bohr (1885-1962)

Bohr formulated the correspondence principle in 1923. which serves as guide in the development of Quantum theory. According to it Quantum theory must become identical with those of classical physics if the dimensions of the system under consideration tend to approach the dimensions of classical systems.

Quantum Mechanics development took place in two stages.

The first stage began with Max Plank's hypothesis in 1900 that radiation is emitted or absorbed by matter in discrete packets or quanta, each of energy hν , where ν is the frequency of radiation and h is plank's constant(h=6.626×10-34 J-s). The theory consisted of classical and non-classical( i.e. semi-classical) concepts, and was not completely satisfactory.

The second stage began with the development of wave mechanics by Erwin Schrodinger in 1926. this mechanics combines earlier ideas of classical wave theory with Louis de-Broglie's wave particle duality relationship.

Now What you have learnt?

DIFFERENCE BETWEEN QUANTUM MECHANICS AND CLASSICAL

MECHANICS

1.CLASSICAL MECHANICS deals with particles/objects of macroscopic size whereas

QUANTUM MECHANICS deals with particles of microscopic size.

2. Classical mechanics which is also known as Newtonian mechanics has been developed on the basis of Newton's law of motion having basic equation(F=ma)

whereas method of approach to obtain the laws of motion in Quantum mechanics is on the basis of Schrodinger's wave equation whose one dimensional time dependent S.W.E form is given by

where Ψ is wave function associated with the particle

n motion and U is the potential energy of the particle.

3.In Classical Mechanics, the future behaviour(i.e. the position and momentum) of a particle can be completely known if its initial position and momentum as well as the forces acting on it are known.

In Quantum Mechanics there is an inherent uncertainty in the determination of initial position and momentum of the particle. It is therefore not possible to completely describe the future position and momentum of a particle without any uncertainty.

4.Classically the trajectory of the particle is sharply defined In Quantum Mechanically the trajectory of the particle is not sharply defined.

5. Classical Mechanics deals with certainties In Quantum Mechanics deals with

probabilities.

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