Physics 410 Quantum Mechanics Fall 2010

Homework #8

due Friday, November 12, 2010

Griffths problems A.17 (prove it in general, do not just give an example) A.19, A.21, A.22 , A.25, A.27(a), 3.4 (a-c), + the following:

Johnson 8.1 Consider the matrix H = . Find its eigenvalues and eigenvectors. (There will be only two.) Show explicitly that the eigenvectors are orthogonal. Construct a unitary matrix that will diagonalize H. Multiply out U^† H U and show explicitly it is diagonal.

Johnson 8.2 The same as problem 8.1, only with the matrix G = . Are the eigenvalues real or complex?

Johnson 8.3 Transform G into the eigenbasis of H, that is, compute U^† G U using U from problem 8.1.

Extra crediti: Griffiths problem A.28