# Influence of the Relative Phase in the de Broglie-Bohm Theory

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Does the possibility exist for motion of a quantum particle to occur when the particle density, given by the square of the Schrödinger wavefunction, is not time-dependent? This question is answered in this Demonstration. A system with two degrees of freedom assigned by a superposition of two stationary eigenfunctions that has commensurate energy eigenvalues can exhibit motion in the associated de Broglie–Bohm theory, provided that the constant phases and are not zero or integer multiples of . The origin of the motion lies in the relative phase of the total wavefunction, which has no classical analogue in particle mechanics. As an example a wavefunction for a quantum isotropic harmonic oscillator is chosen: , where is the Hermite polynomial and , are arbitrary constants. In this case the squared wavefunction (particle density ) is not time-dependent:

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Contributed by: Klaus von Bloh (March 2011)

Open content licensed under CC BY-NC-SA

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"Influence of the Relative Phase in the de Broglie-Bohm Theory"

http://demonstrations.wolfram.com/InfluenceOfTheRelativePhaseInTheDeBroglieBohmTheory/

Wolfram Demonstrations Project

Published: March 7 2011