# Foundation of Quantum Mechanics | Development and Shortcomings

## Inadequacy of Classical Mechanics

The development of **classical mechanics** is based on **Newton's 3 laws** (i) The Law of Inertia, (ii) the law of force and (iii) the law of action and reaction. These laws include the concept of absolute mass, absolute space and absolute time. The * classical mechanics* explain correctly the motion of classical bodies like planets, stars and macroscopic as well as microscopic terrestrial bodies moving with non relativistic speeds. The inadequacy of classical mechanics are :

It cannot explain the non relativistic motion of

**atoms**, electrons and protons etc.It cannot explain the stability of atoms.

It cannot explain observed spectrum of black body radiations.

It cannot explain the observed variation of specific heat of metals and gases.

It cannot explain the origin of discrete spectra of atoms because according to classical mechanics the energy changes are always continuous.

In spite of this classical mechanics could not explain a large number of observed phenomenon like photoelectric effect, Compton effect, Raman effect etc. The inadequacy of Classical Mechanics or Newtonian mechanics led to the development of **Quantum Mechanics**.

## Development of old Quantum Theory

Planck was able to explain law of distribution of energy in the spectrum of black body. This theory was given by Planck in his historic paper titled "Theory of Law of distribution of energy in a normal Spectrum" presented, before the Berlin Academy of Science on December 14, 1900. This day, in fact may be considered at the birthday of * Quantum Mechanics*.

In 1900, Max planck introduced the concept of quantum of energy to explain the phenomenon of black body radiation. He considered that the energy exchange between radiation and its surrounding takes place in quantized amount.

In 1905, Einstein considered that light itself is made of discrete packets of energy.

By introduction of Photon concept, Einstein explained photo electric effect.

In 1913, Neels Bohr introduce model of H atom. He considered that atoms can be found only in discrete states of energy and emission or absorption 0°C radiation by atoms takes places only in discrete amount of hv, because it results from transition of atom between its various energy states.

In 1923 by Compton experiment, He confirmed the corpuscular aspect of light.

In 1923, De broglie postulated that not only radiation exhibit particle like behaviour but also material particle themselves show wave like behaviour.

## Shortcomings of old Quantum Theory

The quantum theory based on **Bohr's quantum** condition and Wilson sommerfeld quantization rule for periodic systems explain only certain limited problems like energy states of hydrogen atom, particle in a box, harmonic oscillator and rigid rotator etc. Main shortcomings of old Quantum theory are :

It could not be applied to non-periodic systems.

It could not explain the spectral lines of relatively simple cases like hydrogen molecule and normal helium atom.

It could not explain the relative intensities of spectral lines at all.

It could not explain the processes connected with the spin of the electrons and Pauli's exclusion principal.

Bohr's postulate of discrete, non radiating energy states on which old quantum theory is based, was empirical without having any theoretical ground.

The above difficulties have been resolved by development of new methods of approach, the * Wave Mechanics* and mathematical forms of the same theory

*. This will be discussed in due course.*

**Matrix Mechanics**