Introduction to Quantum Mechanics 2

1Schrödinger’s Equation and its Applications

General objective

The general objective is to apply the Schrödinger equation to the study of simple physical systems.

Specific objectives

On completing this chapter, the reader should be able to:

• – know the properties of the square-summable wave functions;
• – know the boundary conditions imposed to any square-summable wave function;
• – distinguish between a physical state in classical mechanics and in quantum mechanics;
• – describe a physical quantity in quantum mechanics;
• – define an operator;
• – define an observable;
• – give examples of operators and observables;
• – know the correspondence principle or rule;
• – define the Hamiltonian of a physical system;
• – express the time-dependent Schrödinger equation;
• – express the stationary Schrödinger equation;
• – know the properties of the Schrödinger equation;
• – integrate the Schrödinger equation for a free particle;
• – integrate the Schrödinger equation for the ground state of the hydrogen atom;
• – apply the Schrödinger equation to the study of quantum wells;
• – apply the Schrödinger equation to the study of quantum dots;
• – apply the Schrödinger equation to the study of potential barriers;
• – apply the Schrödinger equation to the study of potential steps;
• – define the probability current;
• – define the reflection and transmission factors;
• – define the reflection and transmission probabilities;
• – provide an interpretation of the tunnel effect;
• – describe the scanning tunneling microscope.

Prerequisites ...