Hi, I've attached the problem as a Picture. I've learned a lot from the help I have received here on Brainmass, and I'm going to try doing this one on myself and hopefully I'll do it right. Thank you for your help!
Consider a simple harmonic oscillator with an angular frequency w. Suppose at t=0 it is in a state given by: (see attachment for equation)
a. Find the normalization constant N
b. What are the possible outcomes of an energy measurement? What are the probabilities associated with each of these outcomes?
c. How does this state evolve in time? In other words find v,t>
d. Find < x > (t) and <p> (t), i.e. find how the average position and momentum changes as a function of time.
Hello and thank you for posting your question to Brainmass.
The solution is attached below in two files. the files are identical in content, only differ in format. The first ...
The solution shows in detail how to normalize the wave function, its time evolution and then how to calculate the position and momentum expectation values using the ladder operators. It shows the result complies with classical interpretation.
States of a Quantum Harmonic Oscillator
6. Consider the state of a harmonic oscillator initially (t=0) to be given by |phi >= 5|0 + 12| 1>.
(a) Find the normalized state.
(b) What will be the state of the particle after time t.
(c) Calculate < x > and < p > for this state at time t. Is this classically what you would expect?