- Calculate the commutator where and .
State the uncertainty principle for and .
A particle of mass is in a 1 dimensional potential . Calculate the rate of change of
the expected values of and , (
Your answer will obviously depend on the state of the particle and on the potential.
- Compute the commutators
and for the 1D harmonic oscillator.
Assume that the states are the eigenstates of the
Hamiltonian with eigenvalues , (
- Prove that
for an arbitrary linear operator .
- For a particle of mass moving in 1-dimension, the Hamiltonian is
. Compute the commutator [H,X] where
is the position operator.
- 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.