Related papers: Problem of a quantum particle in a random potentia…
I review the quantum theory of the electron moving in a random environment. First, the quantum mechanics of individual particles scattered on a random potential is discussed. The quantum-mechanical description is extended to many-body…
We propose a formulation of an absorbing boundary for a quantum particle. The formulation is based on a Feynman-type integral over trajectories that are confined by the absorbing boundary. Trajectories that reach the absorbing wall are…
The problem of a Klein-Gordon particle moving in equal vector and scalar Rosen-Morse-type potentials is solved in the framework of Feynman's path integral approach. Explicit path integration leads to a closed form for the radial Green's…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…
Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
The dynamics of an active, finite-size and immiscible impurity in a dilute quantum fluid at finite temperature is characterized by means of numerical simulations of the projected Gross--Pitaevskii equation. The impurity is modeled as a…
This study aims to address the nature of state change, measurement, and probabilistic outcomes in non-relativistic quantum mechanics. We consider a pair of particles that interact in a one-dimensional setting via a delta-function potential.…
Quantum measurement problem is still unconsensus since it has existed many years and inspired a large of literature in physics and philosophy. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by…
We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave…
While free and weakly interacting particles are well described by a a second-quantized nonlinear Schr\"odinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose…
The Wigner eigenfunctions of a free quantum particle propagating on a plane are derived. Two possibilities are analysed. Firstly, the particle of given energy and angular momentum is discussed. In that case, a special choice of coordinates…
At large quantum numbers, the probability densities for particle-in-a-box or simple harmonic oscillator converge to the classical result upon coarse-graining the quantum mechanical probability densities by introducing a finite resolution in…
We derive an equation for the current of particles in energy space; particles are subject to a mean field effective potential that may represent quantum effects. From the assumption that non-interacting particles imply a free diffusion…
The dynamics of a quantum mechanical particle in a time-independent potential are found to contain many interesting phenomena. These are direct consequences of the (typical) existence of more than one time scale governing the problem. This…
We consider the dynamics of a charged particle interacting with background electromagnetic field under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. Following the prescription in…
A Gedanken experiment is described to explore a counter-intuitive property of quantum mechanics. A particle is placed in a one-dimensional infinite well. The barrier on one side of the well is suddenly removed and the chamber dramatically…
We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…
Stochastic density functional theory is applied to analyze the conductivity of strong two species electrolytes at arbitrary field strengths. The corresponding stochastic equations for the density of the electrolyte species are solved by…
Despite their simplicity, quantum harmonic oscillators are ubiquitous in the modeling of physical systems. They are able to capture universal properties that serve as reference for the more complex systems found in nature. In this spirit,…