Interaction \(\lambda x^ 2_ 1+gx^ 2\) revisited

DOI10.1016/0021-9991(81)90137-6zbMath0457.65066OpenAlexW1485128903MaRDI QIDQ1151250

Andre Hautot

Publication date: 1981

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(81)90137-6

zbMATH Keywords

Schrödinger equationHill determinantnon-perturbative Hill's method

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Ordinary differential operators (34L99)

Related Items (5)

Double exponential sinc-collocation method for solving the energy eigenvalues of harmonic oscillators perturbed by a rational function ⋮ Variational estimates of the energies for the potential \(x^2+\lambda x^2/(1+gx^2)\) ⋮ Applications of the differentiability of eigenvectors and eigenvalues to a perturbed harmonic oscillator ⋮ The exact bound-state ansaetze as zero-order approximations in perturbation theory. II: An illustration: \(V(r)= r^2+ fr^2/ (1+gr^2)\) ⋮ Accurate calculation of the eigenvalues of the \(x^ 2+ \lambda x^ 2/(1+gx^ 2)\) potential

Cites Work

• Convergent solutions of ordinary linear homogeneous difference equations
• An extension of Olver's error estimation technique for linear recurrence relations
• On the interaction of the type λx2/(1+g x2)
• Computational Aspects of Three-Term Recurrence Relations
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