How to derive the Schrodinger equation for a system with position dependent effective mass? For example, I encountered this equation when I first studied semiconductor hetero-structures. All the books that I referred take the equation as the starting point without at least giving an insight into the form of the Schrodinger equation which reads as
[−ℏ22∇1m∗∇+U]Ψ = EΨ.
I feel that it has something to do with conserving the probability current and should use the continuity equation, but I am not sure.
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