Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation: Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras

O. L. Varaksin, V. V. Firstov, A. V. Shapovalov, I. V. Shirokov

Research output: Contribution to journalArticle


The study is continued on noncommutative integration of linear partial differential equations [1] in application to the exact integration of quantum-mechanical equations in a Riemann space. That method gives solutions to the Klein-Gordon equation when the set of noncommutative symmetry operations for that equation forms a quadratic algebra consisting of one second-order operator and of first-order operators forming a Lie algebra. The paper is a continuation of [2], where a single nontrivial example is used to demonstrate noncommutative integration of the Klein-Gordon equation in a Riemann space not permitting variable separation.

Original languageEnglish
Pages (from-to)299-303
Number of pages5
JournalRussian Physics Journal
Issue number3
Publication statusPublished - 1995
Externally publishedYes


ASJC Scopus subject areas

  • Physics and Astronomy(all)

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