Harmonic oscillator with a step and its isospectral properties

被引：1

作者：

Nasuda, Yuta ^{[1
]}

Sawado, Nobuyuki ^{[1
]}

机构：

[1] Tokyo Univ Sci, Dept Phys & Astron, Noda, Chiba 2788510, Japan

来源：

PHYSICA SCRIPTA | 2024年 / 99卷 / 04期

关键词：

exactly solvable models; Schrodinger equation; matching of wavefunctions; piecewise analytic functions; Hermite polynomials; isospectral Hamiltonians; Darboux transformation; SCHRODINGER-EQUATION; QUANTUM-MECHANICS; POTENTIALS; FAMILIES;

D O I：

10.1088/1402-4896/ad2d29

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We investigate the one-dimensional Schrodinger equation for a harmonic oscillator with a finite jump a at the origin. The solution is constructed by employing the ordinary matching-of-wavefunctions technique. For the special choices of a, a = 4l (l = 1, 2, horizontal ellipsis ), the wavefunctions can be expressed by the Hermite polynomials. Moreover, we explore isospectral deformations of the potential via the Darboux transformation. In this context, infinitely many isospectral Hamiltonians to the ordinary harmonic oscillator are obtained.

引用

页数：13

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