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Equivalence of a harmonic oscillator to a free particle and Eisenhart lift. / Dhasmana, Shailesh; Sen, Abhijit; Silagadze, Zurab K.
в: Annals of Physics, Том 434, 168623, 11.2021.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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