I am dealing with an eigenvalue problem whose boundary conditions are also eigenvalue dependent.
Could anyone please comment whether Mathematica can numerically solve such a problem? For boundary condition independent of eigenvalues, I use NDEigenSystem
.
A minimal working example is given here. The eigenvalue problem: −d2ψdx2+x2ψ=Eψ with two boundary conditions: (i) ψ=0 at x=0 and (ii) dψdx+E2ψ=0 at x=1 needs to be solved to calculate the eigenvalues, E, of this operator. This might seem to be a trivial task, but please be aware of the eigenvalue-dependent boundary condition. I would be very thankful if anybody could suggest how to solve such eigenvalue problem in mathematica.
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