Related papers: New Variational Principles in Classical and Semicl…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of…
We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear…
We examine the notion of nonclassicality in terms of quasiprobability distributions. In particular, we do not only ask if a specific quasiprobability can be interpreted as a classical probability density, but require that characteristic…
In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we…
In the classical work by Irving and Zwanzig [Irving J.H. and Zwanzig R.W., J. Chem. Phys. 19 (1951), 1173-1180 ] it has been shown that quantum observables for macroscopic density, momentum and energy satisfy the conservation laws of fluid…
After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics…
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this…
Assume that A is a bounded selfadjoint operator in a Hilbert space H. Then, the variational principle is obtained for some functional. As an application of this principle, a variational principle for the electrical capacitance of a…
In this paper we are going to introduce a new dynamical postulate in Quantum Mechanics. This new principle is defined using path integrals over the set of normalized wave functions. We will show in a qualitative way that this postulate is…
A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the non-relativistic limit) with…
A classical representation for quantum eigenstates of a particle bound in $\lambda z^{2m}$ $(\lambda >0, m=1,2,...)$ potentials is developed. It is represented by ensembles of classical trajectories with energy distributions that can take…
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
We conjecture that the modified commutation relations suggested in the context of quantum gravity (QG) persist also in the classical limit, if the momentum of the classical object is not too large, and calculate the corresponding perihelion…
We formulate a general principle that supplants a Boolean \sigma-algebra of intrinsic properties of a classical system by a \sigma-complex (a union of \sigma-algebras) of extrinsic properties of a quantum system that are elicited by…
We demonstrated that classical mechanics have, besides the well known quantum deformation, another deformation -- so called hyperbolic quantum mechanics. The classical Poisson bracket can be obtained as the limit $h\to 0$ not only of the…
Generalisations of the virial theorm in Classical Mechanics and Quantum Mechanics are examined. It is shown that the generalised virial theorem in Quantum Mechanics leads to certain relations between matrix elements. The differences between…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged…