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## Homework Statement

Evaluate <n|p^2|n>

where p is the momentum operator for the quantised harmonic oscillator.

## Homework Equations

creation operator: a

^{+}|n>=sqrt(n+1)|n+1>

annihilation operator: a|n>=sqrt(n)|n-1>

## The Attempt at a Solution

the operator p can be defined in terms of the creation and annihilation operators, ie. p = (-i/sqrt{2})(a-a

^{+})

I also wrote down that for the quantised harmonic oscillator p = -(ihbar).(partial derivative wrt x) and so p^2= -(hbar)^2.(partial derivative wrt x)^2

I'm stuck on what to do next? How do I evaluate <n|p^2|n> ???

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