## Sample Test Problems

1. The absolute square of a wave function for a free particle is given as:

Find the expected value of as a function of time. Find the expected value of as a function of time. Compute the RMS x-width of this wave packet as a function of time.
2. Find the commutator where is a constant and the second operator can be expanded as .
3. Which of the following are linear operators?
4. For a free particle, the total energy operator H is given by . Compute the commutators [H,x] and [H,p]. If a particle is in a state of definite energy, what do these commutators tell you about how well we know the particle's position and momentum?
5. Find the commutator .
6. Compute the commutator where is the Hamiltonian for a free particle.

Jim Branson 2013-04-22