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## Main Question or Discussion Point

We have a particle in a harmonic oscillator potential. The eigenstates are denoted {|0>,|1>,...,|n>,...}. Initially the particle is in the state |s> = exp(-ipa)|0>, where p is the momentum operator.

I need to find <x> as a function of time using the Heisenberg picture. The problem is, how do I find an expression for |s>? My guess is to express p as p = (some constant)(a- - a+) (where a-/a+ are the ladder operators) and then:

|s> = exp(-i(some constant)(a- - a+)a)|0> = exp(-i(some constant)a)|1>.

But I know this is wrong... What am I supposed to do??

I need to find <x> as a function of time using the Heisenberg picture. The problem is, how do I find an expression for |s>? My guess is to express p as p = (some constant)(a- - a+) (where a-/a+ are the ladder operators) and then:

|s> = exp(-i(some constant)(a- - a+)a)|0> = exp(-i(some constant)a)|1>.

But I know this is wrong... What am I supposed to do??