Prepotential approach to exact and quasi-exact solvabilities |
| |
Authors: | Choon-Lin Ho |
| |
Affiliation: | Department of Physics, Tamkang University, 151 Ying-Chuan Road, Tamsui 251, Taiwan, ROC |
| |
Abstract: | Exact and quasi-exact solvabilities of the one-dimensional Schrödinger 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. |
| |
Keywords: | 03.65.Ca 03.65.Ge 02.30.Ik |
本文献已被 ScienceDirect 等数据库收录! |
|