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Homework Statement
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?
Homework Equations
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.