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Time-dependent Schrödinger equations with effective mass in \((2+1)\) dimensions: intertwining relations and Darboux operators. (English) Zbl 1222.81158

Summary: We construct Darboux transformations for time-dependent Schrödinger equations with position-dependent mass in \((2+1)\) dimensions. Several examples illustrate our results, which complement and generalize former findings for the constant mass case in two spatial variables [A. Schulze-Halberg, “Intertwining relations and Darboux transformations for Schrödinger equations in \((n+1)\) dimensions”, J. Math. Phys. 51, No. 3, Paper No. 033521 (2010)].

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q41 Time-dependent Schrödinger equations and Dirac equations
35Q05 Euler-Poisson-Darboux equations
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