Mapping of Two-Dimensional Schrödinger Equation under the Point Transformation
arXiv:1712.02253 · doi:10.1063/1.4995382
Abstract
For the two-dimensional Schrödinger equation, the general form of the point transformations such that the result can be interpreted as a Schrödinger equation with effective (i.e. position dependent) mass is studied. A wide class of such models with different forms of mass function is obtained in this way. Starting from the solvable two-dimensional model, the variety of solvable partner models with effective mass can be built. Several illustrating examples not amenable to the conventional separation of variables are given.
arXiv comment18 pages
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