Objectives and Homework for September 22, 2005.
[1] Understand the concepts “dispersive medium”, “phase velocity”, and “group velocity”.
[2] Realize that the interpretation of quantum mechanics is a probabilistic one, and realize how probabilities are calculated from matter wave amplitudes.
[3] 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.
[4] Understand the “standard deviation” definition of DQ, where Q is some variable.
[5] Know what the product DxDpx is for a Gaussian wavepacket, and realize that this is its minimum possible value. Hence understand the derivation of the Heisenberg Uncertainty relation between x and px.
[6] Realize that there is no uncertainty relation between variables such as x and py, and realize why.
[7] Know the Heisenberg uncertainty relation between E and t.
[8] Understand the probability interpretation for the wavefunction. Know also how the quantum mechanical wavefunction is similar to the classical electric and magnetic fields, and know how they are different.
[9] Understand what is meant by the term “normalization”, and be able to normalize a wavefunction.
Homework due Friday, September 23, 2005 (as a reminder).
[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.