GRADUATE QUANTUM MECHANICS: 501 Fall 2001 Solution to Assignment 4. 1. (a) For a free particle, H =
p2 2m .
The Heisenberg equations of motion are dx dt dp dt = = 1 p2 p [x, ]= i h 2m m 1 p2 [p, ]=0 i h 2m p t m
From which we deduce that p(t) = p, x(t
GRADUATE QUANTUM MECHANICS: 501 Fall 2001 Assignment 8. Read Shankar Chapter 13. 1. A spin 1 is initially in the state |z, + . The spin is rotated (i) through angle /2 about the y axis, then (ii) 2 through angle /2 about the z axis, and finally (iii) thro