- Calculate the commutator where and .
State the uncertainty principle for and .
**Answer**

*****A particle of mass is in a**1 dimensional potential**. Calculate the rate of change of the expected values of and , ( and ). Your answer will obviously depend on the state of the particle and on the potential.**Answer**

- Compute the commutators
and for the 1D harmonic oscillator.
**Answer**

*****Assume that the states are the eigenstates of the Hamiltonian with eigenvalues , ( ).- a)
- Prove that for an arbitrary linear operator .
- b)
- For a particle of mass moving in 1-dimension, the Hamiltonian is given by . Compute the commutator [H,X] where is the position operator.
- c)
- Compute the mean momentum in the state .

*****At , a particle of mass is in the Harmonic Oscillator state . Use the Heisenberg picture to find the expected value of as a function of time.

Jim Branson 2013-04-22