### Abstract

The free time-dependent Schrödinger equation in three-dimensional space is analyzed as a special case of the wave equation in five-dimensional spacetime. This approach transforms the separation of variables in the parabolic Schrödinger equation into the separation of variables in a nonparabolic equation. Then one can solve the problem using the last theorem of V. N. Shapovalov (see Differents. Uravn., No. 10, 1864 (1980)) on the necessary and sufficient conditions for the complete separation of variables. Other advantages of this approach are also discussed.

Original language | English |
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Pages (from-to) | 600-604 |

Number of pages | 5 |

Journal | Soviet Physics Journal |

Volume | 33 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 1990 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Soviet Physics Journal*,

*33*(7), 600-604. https://doi.org/10.1007/BF00899111

**Free Schrödinger equation analyzed in terms of the wave equation.** / Bagrov, V. G.; Samsonov, B. F.; Shapovalov, A. V.

Research output: Contribution to journal › Article

*Soviet Physics Journal*, vol. 33, no. 7, pp. 600-604. https://doi.org/10.1007/BF00899111

}

TY - JOUR

T1 - Free Schrödinger equation analyzed in terms of the wave equation

AU - Bagrov, V. G.

AU - Samsonov, B. F.

AU - Shapovalov, A. V.

PY - 1990/7

Y1 - 1990/7

N2 - The free time-dependent Schrödinger equation in three-dimensional space is analyzed as a special case of the wave equation in five-dimensional spacetime. This approach transforms the separation of variables in the parabolic Schrödinger equation into the separation of variables in a nonparabolic equation. Then one can solve the problem using the last theorem of V. N. Shapovalov (see Differents. Uravn., No. 10, 1864 (1980)) on the necessary and sufficient conditions for the complete separation of variables. Other advantages of this approach are also discussed.

AB - The free time-dependent Schrödinger equation in three-dimensional space is analyzed as a special case of the wave equation in five-dimensional spacetime. This approach transforms the separation of variables in the parabolic Schrödinger equation into the separation of variables in a nonparabolic equation. Then one can solve the problem using the last theorem of V. N. Shapovalov (see Differents. Uravn., No. 10, 1864 (1980)) on the necessary and sufficient conditions for the complete separation of variables. Other advantages of this approach are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=34249926465&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249926465&partnerID=8YFLogxK

U2 - 10.1007/BF00899111

DO - 10.1007/BF00899111

M3 - Article

AN - SCOPUS:34249926465

VL - 33

SP - 600

EP - 604

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 7

ER -