### Abstract

It is shown that classical and quantum equations of motion of a relativistic spinless particle (the Lorentz and Klein-Gordon equations) allow for a geometrization on the same manifold {Mathematical expression}_{4}. A classical particle on {Mathematical expression}_{4} is described as a free particle ( {Mathematical expression}p^{μ}=0), while the quantum particle, as a free wave ( {Mathematical expression}s=0).

Original language | English |
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Pages (from-to) | 780-783 |

Number of pages | 4 |

Journal | Soviet Physics Journal |

Volume | 33 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 1990 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Simultaneous geometrization of classical and quantum mechanics of spinless particles.** / Korotchenko, K. B.

Research output: Contribution to journal › Article

*Soviet Physics Journal*, vol. 33, no. 9, pp. 780-783. https://doi.org/10.1007/BF00894903

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TY - JOUR

T1 - Simultaneous geometrization of classical and quantum mechanics of spinless particles

AU - Korotchenko, K. B.

PY - 1990/9

Y1 - 1990/9

N2 - It is shown that classical and quantum equations of motion of a relativistic spinless particle (the Lorentz and Klein-Gordon equations) allow for a geometrization on the same manifold {Mathematical expression}4. A classical particle on {Mathematical expression}4 is described as a free particle ( {Mathematical expression}pμ=0), while the quantum particle, as a free wave ( {Mathematical expression}s=0).

AB - It is shown that classical and quantum equations of motion of a relativistic spinless particle (the Lorentz and Klein-Gordon equations) allow for a geometrization on the same manifold {Mathematical expression}4. A classical particle on {Mathematical expression}4 is described as a free particle ( {Mathematical expression}pμ=0), while the quantum particle, as a free wave ( {Mathematical expression}s=0).

UR - http://www.scopus.com/inward/record.url?scp=34249918033&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249918033&partnerID=8YFLogxK

U2 - 10.1007/BF00894903

DO - 10.1007/BF00894903

M3 - Article

VL - 33

SP - 780

EP - 783

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 9

ER -