# 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 ...*

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