Related papers: Sources of quantum waves
This paper addresses the single-valued requirement for quantum wave functions when they are analytically continued in the spatial coordinates. This is particularly relevant for de Broglie-Bohm, hydrodynamic, or stochastic models of quantum…
It is argued that any operational measure of time is inseparably bound to the presence of a periodic process in some medium. Since, as first formulated by Einstein's (1905) equation for the energy, all "particles" (neutrons, electrons,…
We quantise and solve the dynamics of gravitational waves in a quantum Friedmann-Lemaitre-Robertson-Walker spacetime filled with perfect fluid. The classical model is formulated canonically. The Hamiltonian constraint is de-parametrised by…
With an apparent delay of over one century with respect to the development of standard Analytical Mechanics, but still in fully classical terms, the behavior of classical monochromatic wave beams in stationary media is shown to be ruled by…
By using an exact solution to the time-dependent Schr\"{o}dinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source…
This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The…
In this paper I explain how I usually introduce the Schr\"odinger equation during the quantum mechanics course. My preferred method is the chronological one. Since the Schr\"odinger equation belongs to a special case of wave equations I…
The Schrodinger equation based on the de Broglie wave is the most fundamental equation of the quantum mechanics. There can be no doubt about it's prediction validity. However, the probabilistic interpretation on the quantum mechanics has…
Quantum scattering by a one-dimensional odd potential proportional to the square of the distance to the origin is considered. The Schr\"odinger equation is solved exactly and explicit algebraic expressions of the wavefunction are given. A…
We study the global theory of linear wave equations for sections of vector bundles over globally hyperbolic Lorentz manifolds. We introduce spaces of finite energy sections and show well-posedness of the Cauchy problem in those spaces.…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
We establish the uniqueness in the determination of a source term or a coefficient of the zeroth order term of a second-order parabolic equation. Moreover we consider the determination of a potential of the Schr\"odinger equation. For a…
In this paper, we consider a wave equation on a bounded interval where the initial conditions are known (are zero) and we are rather interested in identifying an unknown source term $q(x)$ thanks to the measurement output $y$ which is the…
A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…
Schroedinger's equation gave early quantum theory a visual language that looked like physics again: a wave evolving by a linear differential equation. This essay argues that the same success also seeded a recurring impulse to keep quantum…
An initial-boundary value problem with one boundary condition is considered for the higher order nonlinear Schr\"odinger equation. It is assumed that either the boundary condition is homogeneous or the nonlinearity in the equation is…
This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the…
The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock.…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
Using Schwinger Variational Principle we solve the problem of quantum harmonic oscillator with time dependent frequency. Here, we do not take the usual approach which implicitly assumes an adiabatic behavior for the frequency. Instead, we…