Quadratic algebras applied to noncommutative integration of the KleinGordon equation: Fourdimensional quadratic algebras containing threedimensional nilpotent lie algebras
Abstract
The study is continued on noncommutative integration of linear partial differential equations [1] in application to the exact integration of quantummechanical equations in a Riemann space. That method gives solutions to the KleinGordon equation when the set of noncommutative symmetry operations for that equation forms a quadratic algebra consisting of one secondorder operator and of firstorder 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 KleinGordon equation in a Riemann space not permitting variable separation.
 Publication:

Russian Physics Journal
 Pub Date:
 March 1995
 DOI:
 10.1007/BF00559478
 Bibcode:
 1995RuPhJ..38..299V