HW 9. operators. With solutions

Please turn this in to Michael Saccone's mailbox in the physics department mail room by 5 PM on Friday.
Please click this link to see solutions.
To do this you would need to first watch the videos in the post on raising and lowering operators. (May 29).  The notation is the same as the book.  The ground state is denoted as: \(|0\rangle\).



1. Consider an electron in a 1D harmonic oscillator potential. Suppose the electron is in a state which is an equal mix of the ground state and the first-excited state.
a) Write the time-dependent state in Dirac notation.
b) Calculate \(\langle x \rangle\). Calculate \(\langle p \rangle\).
c) Graph \(\langle x \rangle\) as a function of time.

2. Consider an electron in a 1D harmonic oscillator potential. Suppose the electron is in a state which is an equal mix of the ground state and the second-excited state.
a) Write the time-dependent state in Dirac notation.
b) Calculate \(\langle x^2 \rangle\). Calculate \(\langle p^2 \rangle\).
c) Graph \(\langle x^2 \rangle\) as a function of time.
d) Graph the PE and KE expectation values as a function of time.

3.  Calculate \(\langle x^2 \rangle\) and  \(\langle p^2 \rangle\) for an electron in the nth energy eigenstate of a 1D HO.
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Note: I added two more videos into the post on raising and lowering operators. These videos show how you can calculate a time dependent expectation value.