Related papers: New Variational Principles in Classical and Semicl…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
The correspondence principle states that classical mechanics emerges from quantum mechanics in the appropriate limits. However, beyond this heuristic rule, an information-theoretic perspective reveals that classical mechanics is a…
The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of `absolute space'. When applied to classical mechanics, under the guise of an…
We formulate a variational principle for non-relativistic quantum mechanics inspired by Gauss's principle of least constraint. We define a quantum constraint functional as the probability-weighted square deviation between the actual motion…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and…
We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
A modified lagrangian with causal and retrocausal momenta was used to derive a first causal wave equation and a second retrocausal wave equation using the principle of least action. The retrocausal wave function obtained through this method…
We investigate the possibility that the semiclassical limit of quantum mechanics might be correctly described by a classical dynamical theory, other than standard classical mechanics. Using a set of classicality criteria proposed in a…
A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled Hamilton-Heisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become…
The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction…
In this paper, we establish (1) the classical limit of the Hartree equation leading to the Vlasov equation, (2) the classical limit of the $N$-body linear Schr\"{o}dinger equation uniformly in N leading to the N-body Liouville equation of…
The Schr\"odinger-Robertson inequality for relativistic position and momentum operators X^\mu, P_\nu, \mu, \nu = 0,1,2,3, is interpreted in terms of Born reciprocity and `non-commutative' relativistic phase space geometry. For states which…
In this paper, we define a quantum analogue of the notion of empirical measure in the classical mechanics of $N$-particle systems. We establish an equation governing the evolution of our quantum analogue of the $N$-particle empirical…
The problem of the description of two interacting particles is considered. It is shown that it can be reduced to the description of one particle in an external static potential even in a relativistic case. The method is based on the…
Regarding the limit hbar-->0 as the classical limit of quantum mechanics seems to be silly because hbar is a definite constant of physics, but it was successfully used in the derivation of the WKB approximation. A superseded version of the…
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the $\h \to 0$ asymptotics, it is not yet clear how to explain within standard quantum…