Spiked harmonic oscillators

DOI10.1063/1.1418247zbMath1059.81044arXivmath-ph/0109014OpenAlexW3100105436MaRDI QIDQ4830664

Attila B. von Keviczky, Nasser Saad, Richard L. Hall

Publication date: 14 December 2004

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

Full work available at URL: https://arxiv.org/abs/math-ph/0109014

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 (18)

Spiked oscillators: exact solution ⋮ Convergent and asymptotic expansions of solutions of second-order differential equations with a large parameter ⋮ A new generalization of nonlinear coherent states for the pseudoharmonic oscillator ⋮ Perturbation expansions for a class of singular potentials ⋮ Temporally stable coherent states for a free magnetic Schrödinger operator ⋮ Number-phase entropic uncertainty relations and Wigner functions for solvable quantum systems with discrete spectra ⋮ Study of the generalized quantum isotonic nonlinear oscillator potential ⋮ Study of anharmonic singular potentials ⋮ Quasilinearization approach to computations with singular potentials ⋮ ASYMPTOTIC ITERATION METHOD FOR SINGULAR POTENTIALS ⋮ Accurate analytic presentation of solution of the Schrödinger equation with arbitrary physical potential: excited states ⋮ Comment on ``Supersymmetry and singular potentials by Das and Pernice ⋮ Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials ⋮ Friedrichs extensions of Schrödinger operators with singular potentials ⋮ Spectral functions for the Schrödinger operator on R+ with a singular potential ⋮ Phase coherent states with circular Jacobi polynomials for the pseudoharmonic oscillator ⋮ Green’s function for a Schrödinger operator and some related summation formulas ⋮ Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries

Cites Work

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• Generalized spiked harmonic oscillator
• Singular anharmonicities and the analytic continued fractions. II. The potentials V(r)=a r2+b r−4+c r−6
• Variational and perturbative schemes for a spiked harmonic oscillator
• Elementary bound states for the power-law potentials
• The harmonic oscillator with λx^Mperturbation
• On the eigenvalues of the s-state radial equation of a spiked harmonic oscillator
• On the elementary Schrödinger bound states and their multiplets
• Large-order perturbation expansions for the charged harmonic oscillator
• The nonsingular spiked harmonic oscillator
• Nonperturbative treatment of singular potentials
• Variational analysis for a generalized spiked harmonic oscillator
• Perturbation expansions for the spiked harmonic oscillator and related series involving the gamma function
• Matrix elements for a generalized spiked harmonic oscillator
• A simple numerical method for singular potentials
• Exact Solution of the Schrödinger Equation for Inverse Fourth-Power Potential
• Singular Potentials

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