Constructing Green functions of the Schrödlnger equation by elementary transformations

Gin Yih Tsaur, Jyhpyng Wang

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

The initial value problem in quantum mechanics is most conveniently solved by the Green function method. Instead of the conventional methods of eigenfunction expansion and path integration, we present a new method for constructing the Green functions systematically. By using suitable elementary transformations, one of the conjugate variables in the Hamiltonian can be eliminated and the Green function for the simplified Hamiltonian can be easily derived. We then obtain the Green function for the original Hamiltonian by the reverse sequence of the elementary transformations. The method is illustrated for the linear potential, the harmonic oscillator, the centrifugal potential, and the centripetal barrier oscillator.

Original languageEnglish
Pages (from-to)600-606
Number of pages7
JournalAmerican Journal of Physics
Volume74
Issue number7
DOIs
StatePublished - Jul 2006

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