Prepotential approach: a unified approach to exactly, quasi-exactly, and rationally extended solvable quantal systems
學年 112
學期 2
出版(發表)日期 2024-04-26
作品名稱 Prepotential approach: a unified approach to exactly, quasi-exactly, and rationally extended solvable quantal systems
作品名稱(其他語言)
著者 Choon-Lin Ho
單位
出版者
著錄名稱、卷期、頁數 Physica Scripta 99(6), 060401
摘要 We give a brief overview of a simple and unified way, called the prepotential approach, to treat both exact and quasi-exact solvabilities of the one-dimensional Schrödinger equation. It is based on the prepotential together with Bethe ansatz equations. Unlike the the supersymmetric method for the exactly-solvable systems and the Lie-algebraic approach for the quasi-exactly solvable problems, this approach does not require any knowledge of the underlying symmetry of the system. It treats both quasi-exact and exact solvabilities on the same footing. In this approach the system is completely defined by the choice of two polynomials and a set of Bethe ansatz equations. The potential, the change of variables as well as the eigenfunctions and eigenvalues are determined in the same process. We illustrate the approach by several paradigmatic examples of Hermitian and non-Hermitian Hamiltonians with real energies. Hermitian systems with complex energies, called the quasinormal modes, are also presented. Extension of the approach to the newly discovered rationally extended models is briefly discussed.
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語言 en
ISSN 1402-4896
期刊性質 國外
收錄於 SCI
產學合作
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國別 GBR
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機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/127520 )