Related papers: The Angular Momentum Dilemma and Born-Jordan Quant…
It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schroedinger equation. Here we show…
A which-way measurement in Young's double-slit will destroy the interference pattern. Bohr claimed this complementarity between wave- and particle behaviour is enforced by Heisenberg's uncertainty principle: distinguishing two positions a…
The central limit theorem has been found to apply to random vectors in complex Hilbert space. This amounts to sufficient reason to study the complex valued Gaussian, looking for relevance to quantum mechanics. Here we show that the…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
Recently, a geometric embedding of the classical space and classical phase space of an n-particle system into the space of states of the system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the…
The issue of non-locality in quantum mechanics can potentially be resolved by considering relativistically covariant diffusion in four-dimensional spacetime. Stochastic particles described by the Klein-Gordon equation are shown to undergo a…
Elements of the quantization in field theory based on the covariant polymomentum Hamiltonian formalism (the De Donder-Weyl theory), a possibility of which was originally discussed in 1934 by Born and Weyl, are developed. The approach is…
A complete solution to the long standing problem of basing Schroedinger quantum theory on standard stochastic theory is given. The solution covers all "single" particle three-dimensional Schroedinger theory linear or nonlinear and with any…
We show that following the standard mantra of quantum chemistry and diagonalizing the Born-Oppenheimer (BO) Hamiltonian $\hat H_{\rm BO}(\bm R)$ is not the optimal means to construct potential energy surfaces. A better approach is to…
Newtonian and Scrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
It is shown that Schrodinger's equation and Born's rule are sufficient to ensure that the states of macroscopic collective coordinate subsystems are microscopically localized in phase space and that the localized state follows the classical…
The classical quantization of the motion of a free particle and that of an harmonic oscillator on a double cone are achieved by a quantization scheme [M.C. Nucci, Theor. Math. Phys. 168 (2011) 994], that preserves the Noether point…
Developing an earlier proposal (Ne'eman, Damnjanovic, etc), we show herein that there is a Landau continuous phase transition from the exact quantum dynamics to the effectively classical one, occurring via spontaneous superposition breaking…
In this paper, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a classical quantum molecule involving a possibly large number of nuclei and electrons, described by a Schr\"odinger equation. In the spirit of Born and…
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…
A unique postulate is shown to underly the whole quantum mechanics theory: the invariance of the Heisenberg uncertainty inequality under a group of special nonlinear gauge transformations (NLGT). With this postulate, the quantum mechanics…
We investigate the phase-space dynamics of the Kramers Henneberger (KH) atom solving the time-dependent Schr\"odinger equation for reduced-dimensionality models and using Wigner quasiprobability distributions. We find that, for the…
An effective angular momentum quantization condition of the form $mvr=n\hbar(m/m_F)$ is used to obtain a Bohr-like model of Hydrogen-type atoms and a modified Schr\"{o}dinger equation. Newton's constant, $G$, of Gravitation gets explicitly…
We discuss the quark phase-space or Wigner distributions of the nucleon which combine in a single picture all the information contained in the generalized parton distributions and the transverse-momentum dependent parton distributions. In…
In this paper, I argue that light is a continuous classical electromagnetic wave, while the observed so-called quantum nature of the interaction of light with matter is connected to the discrete (atomic) structure of matter and to the…