A Quasi-Newtonian Approach to Bohmian Mechanics II: Inherent Quantization

TL;DR

This paper demonstrates that in Bohmian mechanics, the eigenvalue postulate naturally arises from continuity conditions, eliminating the need to assume spectra as eigenvalues of operators.

Contribution

It shows that the eigenvalue postulate in quantum mechanics can be derived from Bohmian mechanics without additional assumptions.

Findings

Eigenvalue postulate emerges from continuity conditions

No need to assume spectra as eigenvalues

Bohmian mechanics predicts eigenvalues inherently

Abstract

In a previous paper, we obtained the functional form of quantum potential by a quasi-Newtonian approach and without appealing to the wave function. We also described briefly the characteristics of this approach to the Bohmian mechanics. In this article, we consider the quantization problem and we show that the 'eigenvalue postulate' is a natural consequence of continuity condition and there is no need for postulating that the spectrum of energy and angular momentum are eigenvalues of their relevant operators. In other words, the Bohmian mechanics predicts the 'eigenvalue postulate'.