Applied Quantum Mechanics

Applied Quantum Mechanics

The harmonic oscillator (qualitative) – Barrier penetration and quantum tunnelling (qualitative) – Tunneling microscope - Resonant diode - Finite potential wells (qualitative) - Bloch's theorem for particles in a periodic potential – Basics of kroning - Penney model and origin of energy bands.

Introduction

• In quantum mechanics, the wave function of a system gives the description of that system. We apply Schrodinger's wave equation to a system and then solve it to find the wave function of the system.

• We shall study how Schrodinger's time independent wave equation can be applied to a system and then solved to find the energy and wave function of the system under given conditions.

• We also aim at learning characteristic properties of solutions of this equation and comparing the predictions of quantum mechanics with those of Newtonian mechanics.

• As simple applications of Schrodinger's time independent wave equation, here we shall discuss the problems of:

- Harmonic oscillator

- Barrier penetration and Quantum tunneling

- Finite potential wells