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Equivalence of a harmonic oscillator to a free particle and Eisenhart lift. / Dhasmana, Shailesh; Sen, Abhijit; Silagadze, Zurab K.

In: Annals of Physics, Vol. 434, 168623, 11.2021.

Research output: Contribution to journal › Article › peer-review

Harvard

Dhasmana, S, Sen, A & Silagadze, ZK 2021, 'Equivalence of a harmonic oscillator to a free particle and Eisenhart lift', Annals of Physics, vol. 434, 168623. https://doi.org/10.1016/j.aop.2021.168623

APA

Dhasmana, S., Sen, A., & Silagadze, Z. K. (2021). Equivalence of a harmonic oscillator to a free particle and Eisenhart lift. Annals of Physics, 434, [168623]. https://doi.org/10.1016/j.aop.2021.168623

Vancouver

Dhasmana S, Sen A, Silagadze ZK. Equivalence of a harmonic oscillator to a free particle and Eisenhart lift. Annals of Physics. 2021 Nov;434:168623. doi: 10.1016/j.aop.2021.168623

Author

Dhasmana, Shailesh ; Sen, Abhijit ; Silagadze, Zurab K. / Equivalence of a harmonic oscillator to a free particle and Eisenhart lift. In: Annals of Physics. 2021 ; Vol. 434.

BibTeX

@article{db343d20c78340deafbffe55bec7358b,
title = "Equivalence of a harmonic oscillator to a free particle and Eisenhart lift",
abstract = "It is widely known in quantum mechanics that solutions of the Schr{\"o}dinger equation (SE) for a linear potential are in one-to-one correspondence with the solutions of the free SE. The physical reason for this correspondence is Einstein's principle of equivalence. What is usually not so widely known is that solutions of the Schr{\"o}dinger equation with harmonic potential can also be mapped to the solutions of the free Schr{\"o}dinger equation. The physical understanding of this equivalence is not known as precisely as in the case of the equivalence principle. We present a geometric picture that will link both of the above equivalences with one constraint on the Eisenhart metric.",
keywords = "Classical mechanics, Eisenhart lift, Equivalence principle, Harmonic oscillator, Quantum mechanics",
author = "Shailesh Dhasmana and Abhijit Sen and Silagadze, {Zurab K.}",
note = "Funding Information: We are grateful to Peter Horvathy, Ole Steuernagel, Apostolos Pilafts and Kiyoshi Shiraishi for useful correspondence. The work is supported by the Ministry of Education and Science of the Russian Federation . Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2021",
month = nov,
doi = "10.1016/j.aop.2021.168623",
language = "English",
volume = "434",
journal = "Annals of Physics",
issn = "0003-4916",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Equivalence of a harmonic oscillator to a free particle and Eisenhart lift

AU - Dhasmana, Shailesh

AU - Sen, Abhijit

AU - Silagadze, Zurab K.

N1 - Funding Information: We are grateful to Peter Horvathy, Ole Steuernagel, Apostolos Pilafts and Kiyoshi Shiraishi for useful correspondence. The work is supported by the Ministry of Education and Science of the Russian Federation . Publisher Copyright: © 2021 Elsevier Inc.

PY - 2021/11

Y1 - 2021/11

N2 - It is widely known in quantum mechanics that solutions of the Schrödinger equation (SE) for a linear potential are in one-to-one correspondence with the solutions of the free SE. The physical reason for this correspondence is Einstein's principle of equivalence. What is usually not so widely known is that solutions of the Schrödinger equation with harmonic potential can also be mapped to the solutions of the free Schrödinger equation. The physical understanding of this equivalence is not known as precisely as in the case of the equivalence principle. We present a geometric picture that will link both of the above equivalences with one constraint on the Eisenhart metric.

AB - It is widely known in quantum mechanics that solutions of the Schrödinger equation (SE) for a linear potential are in one-to-one correspondence with the solutions of the free SE. The physical reason for this correspondence is Einstein's principle of equivalence. What is usually not so widely known is that solutions of the Schrödinger equation with harmonic potential can also be mapped to the solutions of the free Schrödinger equation. The physical understanding of this equivalence is not known as precisely as in the case of the equivalence principle. We present a geometric picture that will link both of the above equivalences with one constraint on the Eisenhart metric.

KW - Classical mechanics

KW - Eisenhart lift

KW - Equivalence principle

KW - Harmonic oscillator

KW - Quantum mechanics

UR - http://www.scopus.com/inward/record.url?scp=85116344191&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2021.168623

DO - 10.1016/j.aop.2021.168623

M3 - Article

AN - SCOPUS:85116344191

VL - 434

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

M1 - 168623

ER -

ID: 34377367