Basic Quantum Mechanics

Basic Quantum Mechanics

Photons and light waves - Electrons and matter waves – Compton effect – The Schrodinger equation (Time dependent and time independent forms) - meaning of wave function - Normalization - Free particle - particle in a infinite potential well: 1D, 2D and 3D Boxes – Normalization, probabilities and the correspondence principle

Introduction

• The most outstanding development in modern science is the conception of quantum mechanics. The quantum mechanics is better than Newtonian classical mechanics in explaining the fundamental physics.

• The fundamental concepts were not different from those of everyday experience, such as particle, position, speed, mass, force, energy and even field. These concepts are referred as 'classical’.

• The world of atoms cannot be described and understood with these concepts. For atoms and molecules, the ideas and concepts used in dealing with optics in day to day life is not sufficient. Thus, it needed new concepts to understand the properties of atoms.

• A group of scientists Neils Bohr W. Heisenberg, E Schrodinger, P.A.M. Dirac, W. Pauli, and M. Born conceived and formulated these new ideas in the beginning of 20th century. This new formulation, a branch of physics, was named as quantum mechanics.

Limitations of Classical Mechanics

• The classical physics is complete and beautiful in explaining daily experiences where big bodies are involved. But it breaks down severely at subatomic level and failed to explain some of the phenomenon totally.

• The phenomenas which classical physics failed to explain are black body radiation, photoelectric effect, emission of X-rays, etc.

• In classical - physics, a body which is very small in comparison with other body is termed as 'particle' whereas in quantum mechanics, the body which cannot be divided further is termed as 'particle'.

• The other main difference is the quantized energy state. In classical physics, an oscillating body can assume any possible energy. On the contrary, quantum mechanics says that it can have only discrete non-zero energy.

Need of Quantum Mechanics

• Classical mechanics successfully explained the motions of object which are observable directly or by instruments like microscope.

But when classical mechanics is applied to the particles of. atomic levels, it fails to explain actual behaviour. Therefore, the classical mechanics cannot be used to explain in atomic level, e.g. motion of an electron in an atom.

• The phenomena of black body radiation, photoelectric effect, emission of X-rays, etc. were explained by Max Planck in 1900 by introducing the formula

where, n = 0, 1, 2, ...

h = Planck's constant = 6.63 × 10-34 J/s

• This is known as 'quantum hypothesis’ and marked the beginning of modern physics. The whole microscopic world obeys the above formula.