- A 1D harmonic oscillator is in a linear combination of the energy eigenstates
Find the expected value of .
Answer
- Assuming represents the 1D harmonic oscillator energy eigenstate,
calculate
.
Answer
- Evaluate the ``uncertainty'' in for the 1D HO ground state
where
.
Similarly, evaluate the uncertainty in for the ground state.
What is the product
?
Answer
Its easy to see that either from the integral or using operators.
I'll use operators to compute the rest.
- Use the commutator relation between and to derive .
Now show that is the lowering operator for the harmonic oscillator energy.
- At , a one dimensional harmonic oscillator is in the state
.
Calculate the expected value of as a function of time.
- At , a harmonic oscillator is in a linear combination of the and states.
Find
and
as a function of time.
- A 1D harmonic oscillator is in a linear combination of the energy eigenstates
Find
.
Jim Branson
2013-04-22