第一类PschlTeller势的非线性代数结构

NONLINEAR ALGEBRAIC CONSTRUCTION FOR FIRST P?SCHL-TELLER POTENTIAL*

在形变李代数理论的基础上 ,利用哈密顿算符和自然算符 ,构造出第一类P schl Teller势的非线性谱生成代数 .该非线性代数能够完全确定势场的能量本征态集合和本征值谱 ,在适当的非线性算符变换下可以化为谐振子代数 。

Based on the theory of deformed Lie algebra, we construct a nonlinear spectrum generating algebra for the first Pschl Teller potential by use of the Hamiltonian and the natural operators. This nonlinear algebra can determine the energy spectrum and the complete set of eigenfunctions, and can be converted into the harmonic oscillator algebra through a nonlinear transformation, which shows there is a new symmetry in the system.