量子力学中的新发现──谱问题的部分代数化  

NEW FINDINGS IN QUANTUM MECHANICS---Partial Algebrization of the Spectral Problems

作　　者：时万钟[1] 

机构地区：[1]郑州大学物理系

出　　处：《郑州大学学报（理学版）》1994年第2期38-49,共12页Journal of Zhengzhou University:Natural Science Edition

摘　　要：讨论了新近发现的一类新的谱问题——准严格可解问题，该问题存在的原因是系统的Ｈａｍｉｌｔｏｎｉａｎ存在着隐蔽的动力学对称性。对于一维运动该隐蔽对称性是ＳＵ（２）群。允许部分谱代数化的最简单的一维系统是具有ｘ￣６势且ｘ￣２与ｘ￣６项前系数有某种关系的非谐振子系；本文通过此最简单的一维系统展示求解此类问题的一般方法与步骤．A new class of spectral problems discovered recently the quasi-exactly-solvable prob-lems is discussed,The reason explaining the existence of the problems is a hidden dynamical symme-try present in the Hamiltonian of the system. For one一dimensional motion this hidden symmetry isSU(2),The simplest one一dimensional system admitting algebrization for a part of the spectrum isthe an harmonic oscillator with the anharmonicity x￣6 and a relation between the coefficients is frontof x￣2 and x￣6. A general procedure of solving this class problem in the simplest onedimensional sys-tem is exhibited.

关 键 词：准严格可解问题 隐蔽的动力学对称性 虚相“规范”变换 非齐次多项式空间 微分实现 

分 类 号：O413.1[理学—理论物理]