A note on the eigenvalues of the Hamiltonian of the harmonic oscillator perturbed by the potential \(\lambda x^2/(1+gx^2)\)

DOI10.1016/0034-4877(96)89768-0zbMath0891.34079OpenAlexW2013337673MaRDI QIDQ1373523

Silvestro Fassari

Publication date: 3 August 1998

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0034-4877(96)89768-0

zbMATH Keywords

eigenvaluesHamiltonianFredholm determinantharmonic oscillatorBirman-Schwinger kernel

Mathematics Subject Classification ID

General spectral theory of ordinary differential operators (34L05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

Related Items

The quantum harmonic oscillator on the sphere and the hyperbolic plane, On the eigenvalues of the Hamiltonian of the harmonic oscillator with the interaction \(\lambda x^2/(1+gx^2)\). II, Double exponential sinc-collocation method for solving the energy eigenvalues of harmonic oscillators perturbed by a rational function, A note on the discrete spectrum of Gaussian wells. I: The ground state energy in one dimension

Cites Work

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• On the bound state of Schrödinger operators in one dimension
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• Asymptotic eigenvalue degeneracy for a class of one-dimensional Fokker–Planck operators
• On the interaction of the type λx2/(1+g x2)