About the proof that the s-wave functions of the hydrogen atom obey the Ehrenfest equation of motion

Applying the concept of quantum hydrodynamics on a hydrogen atom, one can derive an equation of motion which describes the time derivative of the mass current density for the relative motion of the electron and the proton. Since this derivation can be performed with the Ehrenfest theorem, we call th...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 869; no. 1; pp. 12007 - 12010
Main Authors Renziehausen, K, Barth, I
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.07.2017
Subjects
Equations of motion
Fluid mechanics
Hydrodynamics
Physics
Protons
Quantum mechanics
Schrodinger equation
Wave functions
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Summary:Applying the concept of quantum hydrodynamics on a hydrogen atom, one can derive an equation of motion which describes the time derivative of the mass current density for the relative motion of the electron and the proton. Since this derivation can be performed with the Ehrenfest theorem, we call this equation the Ehrenfest equation of motion. As quantum hydrodynamics is consistent with Schrödinger's quantum mechanics, the stationary s-wave functions satisfy both the Schrödinger equation and the Ehrenfest equation of motion. It is the purpose of this paper to prove that the stationary s-wave functions satisfy the Ehrenfest equation of motion. From the quantum hydrodynamical point of view, this result for s-wave functions can be interpreted that the Coulomb force density that attracts the electron to the proton is compensated by a quantum force density that is related to the dispersion of the probability density.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/869/1/012007