# QM: expectation value of a harmonic oscillator

first post! but for bad reasons lol

Im trying to find <x> and <p> for the nth stationary state of the harmonic potential: V(x)=(1/2)mw^2x^2

i solved for x: x=sqrt(h/2mw)((a+)+(a-))
so <x> integral of si x ((a+)+(a-)) x si.
therefor the integral of si(n+1) x si + si(n-1) x si.
si(n+1) x si as far as I know is always 0 so this would mean <x>=0?
this same convention would be used for <p>.

sorry for the sloppy work but I'm pretty sure <x>, and <p> shouldnt = 0

nrqed
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Gold Member
first post! but for bad reasons lol

Im trying to find <x> and <p> for the nth stationary state of the harmonic potential: V(x)=(1/2)mw^2x^2

i solved for x: x=sqrt(h/2mw)((a+)+(a-))
so <x> integral of si x ((a+)+(a-)) x si.
therefor the integral of si(n+1) x si + si(n-1) x si.
si(n+1) x si as far as I know is always 0 so this would mean <x>=0?
this same convention would be used for <p>.

sorry for the sloppy work but I'm pretty sure <x>, and <p> shouldnt = 0

$$\langle n| a | n\rangle = \langle n | a^\dagger | n \rangle = 0$$