# Expectation Values For Various States On A Harmonic Oscillator

See the attached file.

3. (a) Calculate the expectation values < x >, < p >, < x^2 > and < p^2 > for the ground state, | 0 >, and the first excited state, | 1 >, of the harmonic oscillator.

(b) Now compute delta(x)delta(p), does this satisfy the uncertainty principle?

4. Using the results from (3), find the expectation values of kinetic, <K> and potential energies, < V >, for the above states, and then that of the total energy, < E >. Are they what you would have expected?

My biggest problem with this homework problem is that I don't know how to do it with the information provided. I have calculated the expectation values in many problems before, but there was more information provided describing the states. Calculating expectation values doesn't usually take me more than a couple minutes, but I just don't know how to approach the problem with the information provided. Thank you very much for your help with this problem!

Note: I have modified this problem to include number 4, because it follows from problem 3. I increased the number of credits for helping with this problem because of that.

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#### Solution Summary

Calculation of expectation values for quantum harmonic oscillator using operator method are presented.