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differential equations - Eigenvalue dependent boundary conditions- mathematica


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) Ïˆ=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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