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Journal of Physics Conference Series

Is Bohm's quantum theory equivalent to standard quantum theory?

Boon Leong Lan, S-N Liang

Published Aug 1, 2008• 0 citations
Publisher

Abstract

It is conventionally believed that Bohm's quanturn theory yields all the predictions of standard quantum theory. However, in this paper, we show that the transmission and reflection coefficients (i.e., probabilities) predicted by Bohm's quanturn theory can be different from those predicted by standard quantum theory for energy eigenstates of the step barrier.

DOI
10.1088/1742-6596/128/1/012017

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It is conventionally believed that Bohm's quanturn theory yields all the predictions of standard quantum theory. However, in this paper, we show that the transmission and reflection coefficients (i.e., probabilities) predicted by Bohm's quanturn theory can be different from those predicted by standard quantum theory for energy eigenstates of the step barrier.
Quantum theory and the de Broglie – Bohm pilot-wave theory are empirically equivalent. In addition to other objections to the pilot-wave theory, many physicists (and some philosophers) take this to be enough to dismiss the pilot-wave theory, as they say it adds nothing to the standard theory. In this short paper I review some objections and replies to the pilot-wave theory. In particular I respond to the empirical equivalence challenge arguing that, given their mutual relationship, there is no reason to expect the two theories to make different predictions, even if they actually might.
The de Broglie-Bohm interpretation was built to perform the same statistical predictions as a standard quantum theory in every conceivable physical situation, and the two theories cannot be distinguished. In this study, the trajectories of crossed photon pairs were examined, and different results were obtained under certain conditions even when there were no differences in the statistical measurements. The conditions and experimental results showed that the trajectories of photons followed the standard interpretation of quantum theory with high probability.
In this paper, use is made of the tools of analytical mechanics and the concept of operators to obtain the time-independent and time-dependent Schrodinger wave equations for quantum mechanical systems. Derivations are embarked upon of expressions for reflection and transmission coefficients for a particle of mass m as well as of energy E moving under different potential set-ups across step functions, barriers and well functions. The tunneling effect is then discussed. The transmission probability equation obtained in this research has been observed to be more accurate than the transmission probability expression deduced by some researchers in 2014 for a tunneling barrier. This research work finds applications in nuclear magnetic resonance imaging systems, synchrotrons, gyrators, accelerators, and in electrodynamics.