The generalized quantum isotonic oscillator

Abstract

Recently, it has been proved that a nonlinear quantum oscillator, generalization of the isotonic one, is exactly solvable for certain values of its parameters. Here we show that the Schroedinger equation for such an oscillator can be transformed into a confluent Heun equation. We give a very simple and efficient algorithm to solve it numerically, no matter what the values of the parameters are. Algebraic quasi-polynomial solutions, for particular values of the parameters, are found.

18 pages, 2 figures

References in corpus (2)

• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
• A quantum exactly solvable non-linear oscillator related with the isotonic oscillator

Cited by in corpus (13)

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• Generalized quantum isotonic nonlinear oscillator in d dimensions
• Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry
• New quasi-exactly solvable class of generalized isotonic oscillators
• Quasi-exact Treatment of the Relativistic Generalized Isotonic Oscillator
• Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
• Ladder operators and squeezed coherent states of a 3-dimensional generalized isotonic nonlinear oscillator
• Bethe ansatz solutions and hidden $sl(2)$ algebraic structure for a class of quasi-exactly solvable systems
• A report on the nonlinear squeezed states and their non-classical properties of a generalized isotonic oscillator
• Recurrence relations and general solution of the exceptional Hermite equation
• Cubic algebras, induced representations and general solution of the exceptional Laguerre equation $X_1$