2001•Physica ScriptaOpen access

Schrödinger Equation with the PotentialV(r) =Ar-4+Br-3+Cr-2+Dr-1

Shi‐Hai Dong

Abstract

By applying a factorization ansatz to the eigenfunction, an exact analytic solution to the stationary Schrödinger equation in two dimensions is obtained with the potential V ( r ) = Ar -4 + Br -3 + Cr -2 + Dr -1 . The restrictions on the parameters of the studied potential and the angular momentum quantum number m are also presented.

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Key concepts: Physics, Ansatz, Eigenfunction, Schrödinger equation, Angular momentum, Mathematical physics, Factorization, Dirac equation