Bohm potential for the time dependent harmonic oscillator
Francisco Soto-Eguibar, Felipe A. Asenjo, Sergio A. Hojman, H\'ector, M. Moya-Cessa
TL;DR
This paper explores the Bohm potential in the Madelung-Bohm formulation of quantum mechanics, demonstrating its relation to a time-dependent harmonic oscillator through a phase satisfying an Ermakov equation.
Contribution
It establishes a connection between the Bohm potential and the Ermakov equation for a quadratic phase in the Madelung-Bohm approach.
Findings
Bohm potential corresponds to a time-dependent harmonic oscillator.
The phase's time dependence must satisfy an Ermakov equation.
Provides a new perspective on quantum dynamics in the Madelung-Bohm framework.
Abstract
In the Madelung-Bohm approach to quantum mechanics, we consider a (time dependent) phase that depends quadratically on position and 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.
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