Intertwined Hamiltonians in two-dimensional curved spaces

被引：49

作者：

Samani, KA ^{[1
]}

Zarei, M ^{[1
]}

机构：

[1] Isfahan Univ Technol, Dept Phys, Esfahan 84156, Iran

来源：

ANNALS OF PHYSICS | 2005年 / 316卷 / 02期

关键词：

intertwining; 2D surfaces;

D O I：

10.1016/j.aop.2004.11.002

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS(2)), de Sitter plane (dS(2)), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：466 / 482

页数：17

共 14 条

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AGHABABAEISAMAN.A, 2002, MOD PHYS LETT A, V17, P131

[2] General methods for constructing bispectral operators [J].