Variational and perturbative schemes for a spiked harmonic oscillator

DOI10.1063/1.528832zbMath0711.47032OpenAlexW2028154851MaRDI QIDQ3496815

V. C. Aguilera-Navarro, R. Guardiola, G. A. Estévez

Publication date: 1990

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

Full work available at URL: http://hdl.handle.net/11449/130408

zbMATH Keywords

diagonalizing symmetric matricesfunctional space spanned by the solutions of the Schrödinger equation for the linear harmonic oscillator Hamiltonian supplemented by a Dirichlet boundary conditionvariational analysis of the spiked harmonic oscillator Hamiltonian operator

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Perturbation theory of linear operators (47A55) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (23)

Spiked oscillators: exact solution ⋮ Variational spiked oscillator ⋮ Unified QLM for regular and arbitrary singular potentials ⋮ Eigenvalues of Schrödinger operators with definite and indefinite weights ⋮ Calculation of the spiked harmonic oscillators through a generalized pseudospectral method ⋮ Spiked Harmonic Oscillator: N^-1 Expansion ⋮ Spiked harmonic oscillators ⋮ Nonperturbative treatment of singular potentials ⋮ Infinite square well with a sinusoidal bottom: a candidate for the Klauder phenomenon? ⋮ WKB and exact wave functions for inverse power-law potentials ⋮ Accurate calculation of the bound states of Hellmann potential ⋮ The convergence of a new symmetric iterative splitting method for non-autonomous systems ⋮ Vibrational-rotational analysis of supersingular plus quadratic \(A/r^ 4+r^ 2\) potential ⋮ An efficient iterative algorithm for solving non-linear oscillation problems ⋮ Study of anharmonic singular potentials ⋮ Quasilinearization approach to computations with singular potentials ⋮ Accurate analytic presentation of solution for the spiked harmonic oscillator problem ⋮ Accurate analytic presentation of solution of the Schrödinger equation with arbitrary physical potential: excited states ⋮ Matrix elements for a generalized spiked harmonic oscillator ⋮ The nonsingular spiked harmonic oscillator ⋮ Friedrichs extensions of Schrödinger operators with singular potentials ⋮ The spiked harmonic oscillator \(V(r)= r^2+ r^{-4}\) as a challenge to perturbation theory ⋮ Computer algebra and large scale perturbation theory

Cites Work

• Singular perturbation potentials
• Ground State of a Bose System of Hard Spheres
• The Numerov method and singular potentials

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