- #1
unscientific
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Homework Statement
Part (a): Find eigenvalues of X, show general relation of X and show X commutes with KE.
Part (b): Give conditions on V1, V2 and VI for X to commute with them.
Part (c): Write symmetric and antisymmetric wavefunctions. Find energies JD and JE.
Part (d): How are unperturbed and perturbed energy levels related?
Homework Equations
The Attempt at a Solution
Part (a)
The eigenvalues I found are ##\pm 1##, which seems right.
No problem with this showing X commutes with K too.
Part(b)
I'm thinking X will commute with ##x^2##, so this means that V1 and V2 must be functions of ##x^2##.
As for VI, I'm not sure.
Part (c)
For two particles A and B,
Symmetric wavefunction is:
[tex]\frac{1}{\sqrt 2} \left(|u,A>|v,B> + |v,A>|u,B>\right)[/tex]
Anti-Symmetric wavefunction is:
[tex]\frac{1}{2} \left( |u,A>|v,B> - |v,A>|u,B>\right)[/tex]
I'm not sure what ##J_D## and ##J_E## are. I'm guessing ##J_E## is the first order perturbed energy ##<E|V_I|E>##?
Part (d)
The delta function means that ##x_1 = x_2##, so the perturbed energy levels is the same as unperturbed? Not sure why either.