- #1
masudr
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Homework Statement
Use ladder operator methods to determine the kinetic and potential energy of eigenstates of the harmonic oscillator.
Homework Equations
[tex]H=\frac{p^2}{2m} + \frac{1}{2}m\omega x^2[/tex]
[tex]x=\sqrt{\frac{\hbar}{2m \omega}}(a+a^{\dagger})[/tex]
The Attempt at a Solution
So I squared x, and then substituted it in the expression for V:
[tex]\langle n | V | n \rangle[/tex]
I ended up getting [itex]V=\frac{1}{2}(n+\frac{1}{2})\hbar \omega[/itex]. This is one half of the energy expectation, so KE must be the same.
I just don't have any references with me to confirm if this is right. Can anyone tell me? Thanks in advance. I could write out what I got V as, if someone wants, but if the answer is right, there may not be much point.