Exact solutions of the Schrödinger equation for nonseparable anharmonic oscillator potentials in two dimensions
- 1 July 1989
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 30 (7) , 1525-1532
- https://doi.org/10.1063/1.528285
Abstract
An explicit procedure is given to construct exact closed‐form solutions to the time‐independent Schrödinger equation in two dimensions [∇2+λ−w(x,y)]ψ=0, where w(x,y) is a polynomial potential of degree greater than two not separable in Cartesian coordinates. Several examples are discussed for which w(x,y) is a sextic polynomial. As has already been seen in studies of the corresponding one‐dimensional problem, a complete set of eigenvalues and wave functions is not found. However, these closed‐form solutions can be used to check the accuracy and efficiency of numerical algorithms.Keywords
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