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I am trying to solve the following eigenvalue differential equation numerically:
∇2ψ = Eψ
, where the coordinate system is polar coordinates and the boundary condition is ψ(R,Φ)=0, where R is the radius of the disk i am working on.
To solve it I am using a finite difference scheme, but there are some problems. The radial equation is:
(-∂2ψ/∂r2-1/r ∂/∂r + m^2/r^2) = Eψ
But since I am discretizing this differential operator on the interval (0,R), the method I use assumes that ψ(0)=ψ(R)=0, which is not the boundary condition I want. How do I implement the one I want (that the eigenfunction is zero on the boundary of the circular disk)?
∇2ψ = Eψ
, where the coordinate system is polar coordinates and the boundary condition is ψ(R,Φ)=0, where R is the radius of the disk i am working on.
To solve it I am using a finite difference scheme, but there are some problems. The radial equation is:
(-∂2ψ/∂r2-1/r ∂/∂r + m^2/r^2) = Eψ
But since I am discretizing this differential operator on the interval (0,R), the method I use assumes that ψ(0)=ψ(R)=0, which is not the boundary condition I want. How do I implement the one I want (that the eigenfunction is zero on the boundary of the circular disk)?