Exact solutions for radial Schrödinger equations

DOI10.1007/BF00674075zbMath0835.34002OpenAlexW1997424870MaRDI QIDQ1903069

Guido Vanden Berghe, Marnix van Daele, H. E. De Meyer

Publication date: 15 January 1996

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00674075

zbMATH Keywords

three-dimensional Schrödinger equationinfinite set of exact solutions

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) NLS equations (nonlinear Schrödinger equations) (35Q55) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (2)

Analytic solutions of the Schrödinger equation for the modified quartic oscillator ⋮ Two-sided eigenvalue bounds for the spherically symmetric states of the Schrödinger equation

Cites Work

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• Exact energy eigenvalues for the doubly anharmonic oscillator
• The exact bound-state ansaetze as zero-order approximations in perturbation theory. I: The formalism and Padé oscillators
• The exact bound-state ansaetze as zero-order approximations in perturbation theory. II: An illustration: \(V(r)= r^2+ fr^2/ (1+gr^2)\)
• The Schrodinger equation for the f(x)/g(x) interaction
• Shifted 1/N expansion approach to the interaction V(r)=r²+λr²/(1+gr²)
• On the x²+λx²/(1+gx²) interaction
• Exact solutions of the Schrodinger equation (-d/dx²+x²+ λx²/(1 +gx²))ψ(x) =Eψ(x)
• On the moment problem for non-positive distributions
• On the Schrodinger equation for the interaction x²+λx²/(1+gx²)

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