Find the transition probability

tgr042
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Applying an operator
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to an initial state
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can cause it to change into a different state
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, if
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is not an eigenstate of
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. The probability for this transition to occur is
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, where
gif.gif
is called the transition amplitude. Consider the case where the initial state is the
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state of the harmonic oscillator,
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, the final state is the
gif.gif
state of the harmonic oscillator,
gif.gif
, and the operator is
gif.gif
. (
gif.gif
is the position operator.) Find the transition probability from
gif.gif
to
gif.gif
.I really am not even sure where to start...
 
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Look up the eigenfunctions of the harmonic oscillator, operate with the given operator on the initial state, integrate according to the definition of the transition amplitude.
 
When you say on the initial state do you mean when psi(n)=1/sqrt(n) a+ psi(n-1) or do you mean psi(2)=1/sqrt(2) a+ psi(1)
 
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