When both external and quantum forces are experienced

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We have discussed in previous posts the emergence of quantum forces in the proposed local-realistic model and how this process leads to probability densities. We have also introduced external forces and explicitly evaluated the probability densities (in the case if quadratic potentials) when they act alone. In this post we are going to evaluate the probability densisites when both quantum forces and an external force are present. A typical situation is a quadratic potential field with particles emitted from many sources (e.g., a gaussian or plane wave preparation).

Illustration by Lucas Taylor/CERN under Wikimedia Commons, https://commons.wikimedia.org/wiki/File:CMS_Higgs-event.jpg

In this situation, the role of the source momentum in dictating the average motion due to the external force is now played by the quantum momentum, that is,


Following the 2018 arxiv paper the position pdf can be now computed. We start with evaluating the average quantum momentum. Then, we generalize the equations obtained for the quantum-force-only case. As a by-product, we observe that the classical action can be retrieved in this general case as well, thus showing the equivalence with the standard QM picture based on wave functions.

On this basis, we will discuss in future posts the specific features of a few force fields, notably a constant force ("quantum faller") and the quantum harmonic oscillator.

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