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Wavefunction collapse is usually seen as a discontinuous violation of the unitary evolution of a quantum system, caused by the observation. Moreover, the collapse appears to be nonlocal in a sense which seems at odds with General…
Integrals of products of Bessel functions exhibit an intriguing feature: under certain conditions on the parameters specifying the integrand, they vanish identically. We provide a physical interpretation of this feature in the context of…
Our paper [Phys. Rev. A 93, 052512 (2016)], proposing a novel form of single determinant wave function that admits non-idempotent 1-electron density matrices, has recently received a Comment [Phys. Rev. A ??, 0????? (2017)] suggesting a…
We generalize the known solution of the Schr\"odinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the…
In the last few years the hydrodynamic formulation of quantum mechanics, equivalent to the Bohmian equations of motion, has been used to obtain numerical solutions of the Schrodinger equation. Problems, however, have been experienced near…
Analytic representation formulas and power series are developed describing the band structure inside periodic photonic and acoustic crystals made from high contrast inclusions. Central to this approach is the identification and utilization…
Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…
Following the spirit of de Broglie and Einstein, we think the concepts of matter and radiation can be unified. We know a particle propagates like a wave; its motion is described by certain wave equations. At this point, it is not clear what…
Bloch Oscillations (BOs) of quantum particles manifest themselves as periodic spreading and re-localization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit BOs are deeply…
The problem of measurement in quantum mechanics is that the quantum particle in the course of evolution, as described by the linear Schrodinger equation, exists in all of its possible states, but in measuring, the particle is always…
The most puzzling issue in the foundations of quantum mechanics is perhaps that of the status of the wave function of a system in a quantum universe. Is the wave function objective or subjective? Does it represent the physical state of the…
We justify and evaluate backflow-threebody wavefunctions for a two component system of electrons and protons. Based on the generalized Feynman-Kacs formula, many-body perturbation theory, and band structure calculations, we analyze the use…
In this paper we review some known results on the motion of Bloch Oscillators in the crystal momentum representation. We emphasize that the acceleration theorem, as usually stated by most of the authors, is incomplete, but in the case of…
We investigate the meaning of the wave function by analyzing the mass and charge density distribution of a quantum system. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus…
The system of equations for water waves, when linearized about equilibrium of a fluid body with a varying bottom boundary, is described by a spectral problem for the Dirichlet -- Neumann operator of the unperturbed free surface. This…
We present a set of exact system solutions to a model we developed to study wave function collapse in the quantum spin measurement process. Specifically, we calculated the wave function evolution for a simple harmonic oscillator of spin…
The behavior of monochromatic electromagnetic waves in stationary media is shown to be ruled by a frequency dependent function, which we call Wave Potential, encoded in the structure of the Helmholtz equation. Contrary to the common belief…
A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as…
We consider a two-dimensional electron gas with Rashba's spin-orbit interaction and two in-plane potentials superimposed along directions perpendicular to each other. The first of these potentials is assumed to be a general periodic…
Our electronic structure theory for crystalline solids is commonly built on the periodic potential assumption $V(\mathbf r)=V(\mathbf r+\mathbf R)$ for every lattice translation $\mathbf R$, enabling Bloch eigenstates, crystal momentum as a…