Quantum-Mechanical Potentials of Bohm.

C.G. Kuper

Davide Fiscaletti

Pedro Luis Grande, Raul Carlos Fadanelli, Maarten Vos

Quantum mechanics is the most successful theory to describe microscopic phenomena. It was derived in different ways over the past 100 years by Heisenberg, Schrödinger, and Feynman. At the same time, other interpretations have been suggested, including the Bohm-De Broglie interpretation and the so-called Bohmian mechanics. Here, we show that Bohmian mechanics, which utilizes the concept of the Bohm quantum potential, can also serve as a starting point for quantizing classical non-relativistic systems. By incorporating the Bohm quantum potential into the Vlasov framework, we obtain a mean-field theory that captures the corpuscular nature of matter, in agreement with quantum mechanics within the Random Phase Approximation (RPA).

Edward R. Floyd

The relationship between the modified potential and Bohm's quantum-mechanical potential is developed. For a given bound-state energy eigenvalue of the Schr\"odinger equation, the modified potential, which is not unique, describes various possible continuous motions. It is shown that all of the various continuous motions of the same energy eigenvalue do generate the same corresponding Schr\"odinger wave function. The parameters which specify these different continuous motions are identified as hidden variables. The equations of motion for a particle with the modified potential differ from those of Bohm.

Glen Dennis, Maurice A. de Gosson, Basil J. Hiley