### Abstract

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 language | English |
---|---|

Pages (from-to) | 299-303 |

Number of pages | 5 |

Journal | Russian Physics Journal |

Volume | 38 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1995 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Russian Physics Journal*,

*38*(3), 299-303. https://doi.org/10.1007/BF00559478

**Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation : Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras.** / Varaksin, O. L.; Firstov, V. V.; Shapovalov, A. V.; Shirokov, I. V.

Research output: Contribution to journal › Article

*Russian Physics Journal*, vol. 38, no. 3, pp. 299-303. https://doi.org/10.1007/BF00559478

}

TY - JOUR

T1 - Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation

T2 - Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras

AU - Varaksin, O. L.

AU - Firstov, V. V.

AU - Shapovalov, A. V.

AU - Shirokov, I. V.

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84951516811&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951516811&partnerID=8YFLogxK

U2 - 10.1007/BF00559478

DO - 10.1007/BF00559478

M3 - Article

VL - 38

SP - 299

EP - 303

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 3

ER -