Linear Combination of Wavefunctions

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Homework Statement


psiplus = 1/sqrt(2) (psi(1,2) + psi(2,1))
Is PsiPlus an eigenfunction of the Hamiltonian operator? If so, what are the eigenvalues for the energy corresponding to PsiPlus in units of (h^2/(8ma)^2)?


Homework Equations


psiplus = 1/sqrt(2) (psi(1,2) + psi(2,1))

psi12 =2/a sin(Pi*x/a) *sin (2Pi*y/a) (2D Particle in Box)
psi21 =2/a sin(2*Pi*x/a) *sin (Pi*y/a)

The Attempt at a Solution


I don't understand some of the core concepts yet, so I don't know how to approach this problem.
 

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