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Homework Statement
A bound quantum system has a complete set of orthonormal, no-degenerate energy eigenfunctions u(subscript n) with difference energy eigenvalues E(subscript n). The operator B-hat corresponds to some other observable and is such that:
B u(subscript 1)=u(subscript 2)
B u(subscript 2)=u(subscript 1)
B u(subscript n)=0
n>3 or B=3
a) Find the complete orthonormal set of eigenfunctions of the operator B-hat (expand out the eigenvalues of B in terms of u, and do not neglect any solutions)
b) If B is measured and found to have the eigenvalue H, what is the expectation value of the energy in the resulting state?
The Attempt at a Solution
B u(subscript1)=u(subscript2)
B u(subscript 2)=u(subscript1)
(B^2) u*(subscript 2)=u(subscript2)
B^2 =1
B=1
I don't think this is leading anywhere. Please help.