Related papers: Fredholm Method for Podolsky Quantum Wave Function
We analyze gravitaxis of a Brownian circle swimmer by deriving and characterizing analytically the experimentally measurable intermediate scattering function (ISF). To solve the associated Fokker-Planck equation we use a spectral-theory…
Plasmonics has attracted much attention not only because it has useful properties such as strong field enhancement, but also because it reveals the quantum nature of matter. To handle quantum plasmonics effects, ab initio packages or…
The boundary integral method for calculating the stationary states of a quantum particle in nano-devices and quantum billiards is presented in detail at an elementary level. According to the method, wave functions inside the domain of the…
We study the stationary scattering theory for the matrix Schr\"odinger equation on the half line, with the most general boundary condition at the origin, and with integrable selfadjoint matrix potentials. We prove the limiting absorption…
The method of a determination of a quantum wave impedance for an arbitrary piecewise constant potential was developed. On the base of this method both the well-known iterative formula \cite{Khondker_Khan_Anwar:1988} and alternative ways for…
The efficacy and accuracy of Bogomolny's method of the quantum surface of section is evaluated by applying it to the quantization of the motion of a particle in a smooth 2-D potential. This method defines a transfer operator T in terms of…
The finite difference time domain (FDTD) method has been successfully applied to obtain energies and wave functions for two electrons in a quantum dot modeled by a three dimensional harmonic potential. The FDTD method uses the…
The Complex Kohn variational method for electron-polyatomic molecule scattering is formulated using an overset grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense,…
We study the strongly singular volume integral equation that describes the scattering of time-harmonic electromagnetic waves by a penetrable obstacle. We consider the case of a cylindrical obstacle and fields invariant along the axis of the…
We obtain the exact energy spectra and corresponding wave functions of the radial Schr\"odinger equation (RSE) for any (n,l) state in the presence of a combination of psudoharmonic, Coulomb and linear confining potential terms using an…
In this paper, we apply the full new method of quantum theory to study the double-slit diffraction of ${C_{60}}$ molecules. We calculate the double-slit wave functions of ${C_{60}}$ molecules by Schr\"{o}dinger equation, and calculate the…
The determination of ultra-long-range molecular potential curves has been reformulated using the Coulomb Greens function to give a solution in terms of the roots of an analytical determinantal equation. For a system consisting of one…
Frame-dragging effect manifests itself as polarization direction rotation when linearly polarized electromagnetic/gravitational wave scatters from a spinning point source through gravitational interactions, an effect also known as the…
The semiclassical Boltzmann equation is widely used to study transport effects. However, being semiclassical and borrowing heavily from classical mechanics, the formalism calls for verification from the perspective of quantum mechanics.…
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…
In recent times it has been paid attention to the fact that (linear) wave equations admit of "soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized…
This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…
Fredholm integral equations of the first kind are the prototypical example of ill-posed linear inverse problems. They model, among other things, reconstruction of distorted noisy observations and indirect density estimation and also appear…
We investigate the possibility of detecting the Podolsky generalized electrodynamics constant $a$. First we analyze an ion interferometry apparatus proposed by B. Neyenhuis, et al (Phys. Rev. Lett. 99, (2007) 200401) who looked for…
In this work, we investigate how both rotation and a Coulomb potential affect the quantum mechanical description of a spin-$1/2$ particle in the presence of the Aharonov-Bohm effect. We employ the method of the self-adjoint extensions in…