Related papers: Classical Representation for Quantum States of a P…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
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 mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schroedinger equation for them is solved by using a generalized series solution for the bound states (using the Froebenius method) and then an…
Classical electromagnetic radiation from quantum currents and densities are calculated. For the free Schrodinger equation with no external force it's found that the classical radiation is zero to all orders of the multipole expansion. This…
A Lagrangian formulation is constructed for particle interpretations of quantum mechanics, a well-known example of such an interpretation being the Bohm model. The advantages of such a description are that the equations for particle motion,…
We discuss two topics that are usually considered to be exclusively "quantum": the Schroedinger equation, and the uncertainty principle. We show (or rather recall) that the Schroedinger equation can be derived from Hamilton's equations…
A calculation of the classical analogue for the quantum wave function and local denity of states, in energy representation, is presented for simple Hamiltonian systems. Sucha analogous were proposed by M. V. Berry and A. voros considering…
Models of quantum and classical particles on the d-dimensional cubic lattice with pair interparticle interactions are considered. The classical model is obtained from the corresponding quantum one when the reduced physical mass of the…
We solve the stationary Schr\"odinger equation for a particle confined to a 3D spherical wedge -- the region $\{(r,\theta,\phi): 0 \leq r \leq R,\, 0 \leq \theta \leq \pi,\, 0 \leq \phi \leq \Phi\}$ with Dirichlet BCs on all surfaces. This…
The time-dependent Schr\"odinger equation for atomic hydrogen in few-cycle laser pulses is solved numerically. Introducing a positive definite quantum distribution function in energy-position space, a straightforward comparison of the…
From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of…
At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean…
The principle of correspondence (or classical limit) is essential in quantum mechanics. Yet, how and why quantum phenomena vanish at the macroscopic scale are issues still open to debate. Here, quantum mechanical predictions for…
In this paper we address the problem of a particle moving in singular one dimensional potentials in the framework of quantum mechanics with minimal length. Using the momentum space representation we solve exactly the Schrodinger equation…
The problem of a spin-free electron with mass $m$, charge $e$ confined onto a ring of radius $R_0$ and with an attractive Dirac delta potential with scaling factor (depth) $\kappa$ in non-relativistic theory has closed form analytical…
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the…
Efficient representation of quantum many-body states on classical computers is a problem of enormous practical interest. An ideal representation of a quantum state combines a succinct characterization informed by the system's structure and…
We describe both quantum particles and classical particles in terms of a classical statistical ensemble, characterized by a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same…
The angular part of the Schrodinger equation for a central potential is brought to the one-dimensional 'Schrodinger form' where one has a kinetic energy plus potential energy terms. The resulting polar potential is seen to be a family of…
In this work we explore the possibility of quantum bound states in a Schwarzschild gravitational field leveraging the analogy of the elementary derivation of bound states in the Coulomb potential as taught in an undergraduate course in…