GREEN-FUNCTIONS THROUGH SO(2, 1) LIE-ALGEBRA IN NONRELATIVISTIC QUANTUM-MECHANICS

被引：14

作者：

BOSCHI, H ^{[1
]}

VAIDYA, AN ^{[1
]}

机构：

[1] UNIV ESTADUAL PAULISTA,DEPT FIS & QUIM,BR-12500 GUARATINGUETA,SP,BRAZIL

来源：

ANNALS OF PHYSICS | 1991年 / 212卷 / 01期

关键词：

D O I：

10.1016/0003-4916(91)90370-N

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We discuss an algebraic technique to construct the Green's function for systems described by the noncompact so(2, 1) Lie algebra. We show that this technique solves the one-dimensional linear oscillator and Coulomb potentials and also generates particular solutions for other one-dimensional potentials. Then we construct explicitly the Green's function for the three-dimensional oscillator and the three-dimensional Coulomb potential, which are generalizations of the one-dimensional cases, and the Coulomb plus an Aharonov-Bohm potential. We discuss the dynamical algebra involved in each case and also find their wave functions and bound state spectra. Finally we introduce a point canonical transformation in the generators of so(2, 1) Lie algebra, show that this procedure permits us to solve the one-dimensional Morse potential in addition to the previous cases, and construct its Green's function and find its energy spectrum and wave functions. © 1991.

引用

页码：1 / 27

页数：27

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