Related papers: On the path integration for the potential barrier …
We derive an exact expression for the transmission amplitude of a particle moving through a harmonically driven delta-function potential by using the method of continued-fractions within the framework of Floquet theory. We prove that the…
Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing many identical inclusions. Historically, this numerical…
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…
We consider a simple action for a fractional spin particle and a path integral representation for the propagator is obtained in a gauge such that the constraint embodied in the Lagrangian is not an obstacle. We obtain a propagator for the…
The extended boundary condition method can be formulated to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative…
The path integral formulation of quantum mechanics constructs the propagator by evaluating the action S for all classical paths in coordinate space. A corresponding momentum path integral may also be defined through Fourier transforms in…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
We solve the path integral in momentum space for a particle in the field of the Coulomb potential in one dimension in the framework of quantum mechanics with the minimal length given by $(\Delta X)_{0}=\hbar \sqrt{\beta}$, where $\beta$ is…
Invited talk given at the ``International Workshop on `Symmetry Methods in Physics' in memory of Ya.\ A.\ Smorodinsky, 5--10 July 1993, Dubna, Russia; to appear in the proceedings. In this contribution I present further results on steps…
We investigate the propagation of electromagnetic waves through a static wormhole. It is shown that the problem can be reduced to a one-dimensional Schr\"odinger-like equation with a barrier-type potential. Using numerical methods, we…
We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…
We present an explicit path integral evaluation of the free Hamiltonian propagator on the (D-1)-dimensional pseudosphere, in the horicyclic coordinates, using the integral equation method. This method consists in deriving an integral…
We consider the time-independent Wigner functions of phase-space quantum mechanics (a.k.a. deformation quantization) for a Morse potential. First, we find them by solving the $\ast$-eigenvalue equations, using a method that can be applied…
A propagator for the one dimensional time-dependent Schr\"odinger equation with an asymmetric rectangular potential is obtained using the multiple-scattering theory approach. It allows for the consideration of the reflection and…
A separable $x-y$ model is solved for a specialized vector potential (no magnetic and weak electric fields) penetrating slowly\textbf{,} adiabatically into and across a rectangular box to which an electron is confined. The time-dependent…
Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has…
In QFT the effective potential is an important tool to study symmetry breaking phenomena. It is known that, in some theories, the canonical approach and the path-integral approach yield different effective potentials. In this paper we…
A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and…
Path integration for the potential V={\alpha}cos{\theta} is performed. Satisfaction of the corresponding Schr\"odinger equation by the resulting Feynman kernel is demonstrated. Expressions for the related Green function are presented.