Factorization-Algebraization-Path Integration and Dynamical Groups

  • Akira Inomata
  • Raj Wilson

Abstract

Schrödingerl proposed an elegant method of factorization of a quantum-mechanical second-order linear differential equation into a product of two first-order differential operators often referred to as ladder operators. These ladder operators when acting on respective eigenfunctions create new eigenfunctions with a quantum number raised or lowered by one unit. Schrödinger’s method was further systematically studied for a class of second-order linear differential equations in particular by Infeld and Hull2 who have shown that a second-order differential equation which may be brought into the form:
(0.1)
may be factorized into products of two first-order ladder operators such that
(0.2)

Keywords

Path Integral Dynamical Group Unitary Irreducible Representation Kepler Problem Ladder Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Akira Inomata
    • 1
  • Raj Wilson
    • 2
  1. 1.Department of PhysicsState University of New YorkAlbanyUSA
  2. 2.Department of MathematicsUniversity of TexasSan AntonioUSA

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