(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Normalised energy eigenfunction for ground state of a harmonic oscillator in one dimension is:

〈x|n〉=α^(1/2)/π^(1/4) exp(-□(1/2) α^2 x^2)

n = 0

α^2=mω/h

suppose now that the oscillator is prepared in the state:

〈x|ψ〉=σ^(1/2)/π^(1/4) exp(-(1/2) σ^2 x^2)

What is the probability that a measurement of the energy gives the result E_0 = 1/2 hω?

2. Relevant equations

3. The attempt at a solution

I squared both states as that is the probability of the states, but I cannot see where the energy eigenvalue would fit into it.

It probably something glaringly obvious, but I haven't done this in a long time and certainly not with dirac notation. Please help.

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# Normalised Energy Eigenfunction (Probability with Dirac Notation)

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