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Homework Statement
The Hamiltonian for a rigid rotator in the xy plane is H = -hbar^2 / 2I d^2/dphi^2
Find the energy levels and eigenfunctions of H.
The unnormalised wavefn of the rotator at time t=0 is:
psi = 1 + 4sin^2 phi
Find the possible results of a measurement of its energy and their relative probabilities
Homework Equations
The Attempt at a Solution
Ok so I see that the Hamiltonian is basically hbar^2 Lz ^2 / 2I therefore its energy levels are hbar ^2 m^2 / 2I
Also see that its eigenfunctions are psi = A sin mphi + B cos mphi
where normalisation means |A|^2 + |B^2| = 1/pi (is this right..?)
I\'ve decomposed sin^2phi and have written psi (phi) = 3-2cos2phi
I can also normalise this
I see that its a sum of m=0 wavefunction and m=2 wavefunction
but to work out the relative probabilities I need to work out the amplitude <psi m=2|psi>
But my question is: what do I use for |psi m=2>? I don't have the constants A and B..
So how can i work out the amplitude?
bit confused..
thanks!