Related papers: Quantum Particle Statistics in Classical Shallow W…
We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…
We have recently proposed a new general concept of macroscopic quantum-type experiment. It amounts to transform a classical fluid into a quantum-type fluid by the application of a quantum-like potential, either directly in a stationary…
We show that the Schr\"odinger equation can be solved exactly based only on classical least action. Fundamental postulates of quantum mechanics can in turn be derived directly from this construction. The results extend to the relativistic…
Branching flow -- a phenomenon known for steady wave propagation in two-dimensional weak correlated random potential is also present in the time-dependent Schr\"odinger equation for a single particle in one dimension, moving in a…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
We compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum…
A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It…
A recent article by Lohmiller \& Slotine (Proc.\ R.\ Soc.\ A \textbf{482}: 20250413) claims that the Schr\"odinger equation can be solved exactly using only classical least action and classical fluid density, asserting that this formulation…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
We derive the classical equations of hydrodynamic type (Euler equation and the continuity equation) from which the Schrodinger equation follows as a limit case. It is shown that the statistical ensemble corresponding to quantum system and…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component $\phi_j$ of the wave vector is understood as a…
The quantization of gravity coupled to a perfect fluid model leads to a Schr\"odinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic…
We set up the classical wave equation for a particle formed of an oscillatory zero-rest-mass charge together with its resulting electromagnetic waves, traveling in a potential field $V$ in a susceptible vacuum. The waves are…