Bohm potential for the time dependent harmonic oscillator

Francisco Soto-Eguibar; Felipe A. Asenjo; Sergio A. Hojman; Héctor M. Moya-Cessa

doi:10.1063/5.0044144

Bohm potential for the time dependent harmonic oscillator

Francisco Soto-Eguibar, Felipe A. Asenjo, Sergio A. Hojman, Héctor M. Moya-Cessa

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

3 Scopus citations

Abstract

In the Madelung-Bohm approach to quantum mechanics, we consider a time dependent phase that depends quadratically on position, and we show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided the time dependent term in the phase obeys an Ermakov equation.

Original language	English
Article number	122103
Journal	Journal of Mathematical Physics
Volume	62
Issue number	12
DOIs	https://doi.org/10.1063/5.0044144
State	Published - 1 Dec 2021
Externally published	Yes

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title = "Bohm potential for the time dependent harmonic oscillator",

abstract = "In the Madelung-Bohm approach to quantum mechanics, we consider a time dependent phase that depends quadratically on position, and we show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided the time dependent term in the phase obeys an Ermakov equation.",

author = "Francisco Soto-Eguibar and Asenjo, {Felipe A.} and Hojman, {Sergio A.} and Moya-Cessa, {H{\'e}ctor M.}",

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AU - Soto-Eguibar, Francisco

AU - Asenjo, Felipe A.

AU - Hojman, Sergio A.

AU - Moya-Cessa, Héctor M.

PY - 2021/12/1

Y1 - 2021/12/1

N2 - In the Madelung-Bohm approach to quantum mechanics, we consider a time dependent phase that depends quadratically on position, and we show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided the time dependent term in the phase obeys an Ermakov equation.

AB - In the Madelung-Bohm approach to quantum mechanics, we consider a time dependent phase that depends quadratically on position, and we show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided the time dependent term in the phase obeys an Ermakov equation.

UR - http://www.scopus.com/inward/record.url?scp=85122193072&partnerID=8YFLogxK

U2 - 10.1063/5.0044144

DO - 10.1063/5.0044144

M3 - Article

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SN - 0022-2488

VL - 62

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 12

M1 - 122103

ER -

Bohm potential for the time dependent harmonic oscillator

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