(©2009, François G. Amar, All rights reserved)

Summary for Week 3

Reading in Levine: Chapter 17.6 to 17.11

Homework problems

Hand in on Monday, February 2: 17.15, 17.21, 17.22, 17.23, 17.29, 17.31, 17.33, 17.39, 17.40, 17.41

Key Concepts

correspondence principle

operators

eigenfunctions and eigenvalues

postulates of quantum mechanics

square-integrability; expectation values

probability density

Key Equations

Classical to quantum correspondence

Particle in a 1-D box of length a:

V(x) = 0 for 0<x<a

V(x) = infinite for x≤0 or x≥a

Postulates of quantum mechanics:

1. The state of a system is described by a function (state function or wave function), , which is a function of coordinates and time. is single-valued, continuous, and quadratically integrable.

2. For each physical property (energy, momentum, angular momentum,...) of a system, there is an operator, , which can be written down using the correspondence principle:

3. If the property is measured, the only values that will be found are the eigenvalues of as determined by the solutions of the eigenvalue equation: .

4. The expectation value or average value of a property A is given by the integral:

5. The probability of finding a particle in a particular region of space (1-dimensional version) is:

.

 

 

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