\langle n|x|n'\rangle = \sqrt{\frac{\hbar}{2m\omega}}\langle n|(a_++a_-)|n'\rangle = \sqrt{\frac{\hbar}{2m\omega}}[\sqrt{n'+1}\langle n|n'+1\rangle + \sqrt{n'}\langle n|n'-1\rangle] = \sqrt{\frac{\hbar}{2m\omega}}(\sqrt{n'+1}\delta_{n,n'+1} + \sqrt{n'}\delta_{n,n'-1}) = \sqrt{\frac{\hbar}{2m\omega}}(\sqrt{n}\delta_{n',n-1} + \sqrt{n'}\delta_{n,n'-1}).
Added by Lisa M.
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h h (n|x|n')= (n|(a++a-)|n)=V [Vn'+I(n|n'+I)+Vn'(n|n'-I) 2mw 2mu Show more…
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