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<[tex]\Psi[/tex]|[tex]\Psi[/tex]> where the complex conjugate ensures that the answer is real. This means that we're looking at the square of the wave function to determine the probability of finding the particle.

Now to determine the probability of a wave function being in eigenstate n, we use the overlap integral of the wave function and normalised eigenstate (for general harmonic oscillator potential V(x) = 1/2m[tex]\omega[/tex]^{2}x^{2}) over all x. Now I don't understand why we take the square of this answer to find the probability? I know we're not looking for the probability of a position, but an energy eigenstate. I just can't follow where it comes from.

Apologies for not writing out the equation, but the Latex is screwing up for me