Solution of the spectral problem for the Schrödinger equation with a degenerate polynomial potential of even power

DOI10.1007/BF02069892zbMath0940.34068OpenAlexW2037380870MaRDI QIDQ1817646

A. S. Vshivzev, N. V. Norin, Vladimir N. Sorokin

Publication date: 14 March 2000

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02069892

zbMATH Keywords

asymptotic behaviororthogonal polynomialsstationary Schrödinger equationdegenerate potentialMellin convolution integralMittag-Leffler transformspecral theory

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (5)

Superdimensional Metamaterial Resonators From Sub-Riemannian Geometry ⋮ Radial Schrödinger equation: The spectral problem ⋮ Some features of the thermodynamics of nonlinear classical systems ⋮ Some thermodynamic features of ideal systems with nonlinear interaction ⋮ Spectral problem of the radial Schrödinger equation with confining power potentials

Cites Work

• Quantal problems with partial algebraization of the spectrum
• Calculation of the eigenvalues of Schrödinger equations by an extension of Hill's method
• QUASI-EXACTLY-SOLVABLE QUANTAL PROBLEMS: ONE-DIMENSIONAL ANALOGUE OF RATIONAL CONFORMAL FIELD THEORIES
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