- 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. - Find the commutator where is a constant and the second operator can be expanded as .
- Which of the following are linear operators?
- 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?
- Find the commutator .
- Compute the commutator where is the Hamiltonian for a free particle.

Jim Branson 2013-04-22