Prepotential approach to exact and quasi-exact solvabilities

Journal Article · Mon Sep 15 04:00:00 EDT 2008 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2008.04.010· OSTI ID:21163737

Ho, C -L ^[1]

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1. Department of Physics, Tamkang University, 151 Ying-Chuan Road, Tamsui 251, Taiwan (China)

Exact and quasi-exact solvabilities of the one-dimensional Schroedinger equation are discussed from a unified viewpoint based on the prepotential together with Bethe ansatz equations. This is a constructive approach which gives the potential as well as the eigenfunctions and eigenvalues simultaneously. The novel feature of the present work is the realization that both exact and quasi-exact solvabilities can be solely classified by two integers, the degrees of two polynomials which determine the change of variable and the zeroth order prepotential. Most of the well-known exactly and quasi-exactly solvable models, and many new quasi-exactly solvable ones, can be generated by appropriately choosing the two polynomials. This approach can be easily extended to the constructions of exactly and quasi-exactly solvable Dirac, Pauli, and Fokker-Planck equations.

• OSTI ID: 21163737
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 9 Vol. 323; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENFUNCTIONS
EIGENVALUES
EXACT SOLUTIONS
FOKKER-PLANCK EQUATION
ONE-DIMENSIONAL CALCULATIONS
POLYNOMIALS
POTENTIALS
SCHROEDINGER EQUATION