Exact and approximate solutions of the spectral problems for the differential Schrödinger operator with polynomial potential in \(\mathbb{R} ^K\), \(K \geq 2\)

DOI10.1007/S10958-019-04354-2zbMath1432.65063OpenAlexW2954767094MaRDI QIDQ2010187

Yanyan Li

Publication date: 3 December 2019

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-019-04354-2

zbMATH Keywords

Schrödinger operatorspectral problemsfunctional-discrete methodpolynomial potentials

Mathematics Subject Classification ID

Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Eigenvalue problems for linear operators (47A75) Schrödinger operator, Schrödinger equation (35J10) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

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Cites Work

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• Super-exponentially convergent parallel algorithm for eigenvalue problems with fractional derivatives
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• New properties of the FD-method in its applications to the Sturm-Liouville problems
• The FD-method for an eigenvalue problem in a case where the base problem has eigenvalues of arbitrary multiplicities in a Hilbert space
• Exact solutions of the Schrödinger equation for nonseparable anharmonic oscillator potentials in two dimensions
• Introduction to Numerical Continuation Methods
• Exact solutions of a spectral problem for the schrödinger differential operator with polynomial potential in R²

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