Objectives and Homework for September 20, 2005.
[1] Understand what is meant by a wavepacket, and understand how wavepackets necessarily lead to uncertainty relations.
[2] Understand what a Fourier Transform is.
[3] Understand the concepts “dispersive medium”, “phase velocity”, and “group velocity”.
[4] Realize that the interpretation of quantum mechanics is a probabilistic one, and realize how probabilities are calculated from matter wave amplitudes.
[5] Know that the term “wavefunction” refers to a mathematical function used to represent a matter wave. Realize that this function can be a function of any dynamical variable, although functions of space and momentum are most common.
[6] Know what normalization of a wavefunction means, and understand its physical relevance. Given a wavefunction that is not normalized, be able to determine the corresponding normalized wavefunction.
[7] Know that there exist many sets of complementary variables in nature, all of which satisfy uncertainty relations. Be able to describe the physical origin of such uncertainty relations.
Homework due Friday, September 23, 2005.
[1] Read through to the end of Section 5.5 in Thornton & Rex.
[2] Do Problems 4, 13, 21, 23, 25, and 29 at the end of Chapter 5 in Thornton & Rex.