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Remarks on the solution of the position-dependent mass Schrödinger equation. (English) Zbl 1204.81055
Summary: An approximate method is proposed to solve the position-dependent mass (PDM) Schrödinger equation. The procedure suggested here leads to the solution of the PDM Schrödinger equation without transforming the potential function to the mass space or vice versa. The method based on the asymptotic Taylor expansion of the function produces an approximate analytical expression for eigenfunction and numerical results for eigenvalues of the PDM Schrödinger equation. The results show that the PDM and constant mass Schrödinger equations are not isospectral. The calculations are carried out with the aid of a computer system of symbolic or numerical calculation by constructing a simple algorithm.
MSC:
81Q05Closed and approximate solutions to quantum-mechanical equations
82D25Crystals (statistical mechanics)
82C70Transport processes (time-dependent statistical mechanics)
81T80Simulation and numerical modelling (quantum field theory)