Bohmian mechanics in momentum representation and beyond

•Bohmian mechanics is extended onto the momentum representation.•The symmetry in the formulation of Bohmian mechanics between coordinate and momentum representation is proved.•The linear potential is solved by the application of Bohmian mechanics in momentum representation. It is shown how to extend...

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Bibliographic Details
Published in:Physics letters. A 2020-09, Vol.384 (26), p.126671, Article 126671
Main Authors: Bonilla-Licea, Moise, Schuch, Dieter
Format: Article
Language:English
Subjects:
Bohmian mechanics
Momentum representation
Phase space
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Summary:•Bohmian mechanics is extended onto the momentum representation.•The symmetry in the formulation of Bohmian mechanics between coordinate and momentum representation is proved.•The linear potential is solved by the application of Bohmian mechanics in momentum representation. It is shown how to extend Bohmian mechanics to an arbitrary representation, based on the polar form of the wave function. The early criticism of Pauli and Heisenberg concerning the asymmetric role of the position variable in Bohm's approach can be removed by presenting the momentum space version of the theory. It is illustrated that for certain problems, like the motion in a linear position-dependent field, the momentum space representation can be advantageous. This analysis also allows to trace back the origin of the quantum potential to the squaring of complex quantities and the resulting mixing of phase and amplitude.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2020.126671