Related papers: Propagator of a Charged Particle with a Spin in Un…
In the present paper we consider the semiclassical magnetic Schr\"odinger equation, which describes the dynamics of charged particles under the influence of a electro-magnetic field. The solution of the time-dependent Schr\"odinger equation…
In this paper we evaluate the expression for the Green function of a pseudo-classical spinning particle interacting with constant electromagnetic external fields by taking into account the anomalous magnetic and electric moments of the…
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…
Green function and linear integrals of motion for a charged particle moving in electric field are discussed. Wigner function and tomogram of the ststionary states of the charge are obtained. Connection of quantum propagators for Schrodinger…
We propose a method to describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field. We apply the approach to the case of hyperfine interaction with axial symmetry, which can be solved…
We consider the functional Schrodinger equation for a self interacting scalar field in an expanding geometry. By performing a time dependent scale transformation on the argument of the field we derive a functional Schrodinger equation whose…
This work investigates the motion of a non-relativistic charged particle within the spacetime of a global monopole. We introduce the Schr\"odinger equation to describe the particle's motion with two interactions by considering the Kratzer…
We propose integral representations and analytical solutions for the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. We explore the exact Green function and an exact…
The technique of functional integration over velocities is applied to the calculation of the propagator of a spinning particle with and without anomalous magnetic moment. A representation for the spin factor is obtained in this context for…
A general treatment of the quantal time-dependent coupled oscillators in presence of the variable magnetic field is presented. The treatment is based on the use of an alternative canonical transformations, time-dependent unitary…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
The Cauchy problem for the Schr\"odinger equations is studied with time-dependent potentials growing polynomially in the spatial direction. First the existence and the uniqueness of solutions are shown in the weighted Sobolev spaces. In…
We study the non-linear Schr\"{o}dinger equation with time depending magnetic field without smallness assumption at infinity. We obtain some results on the Cauchy problem, WKB asymptotics and instability.
The linear system of differential equations for determination of transmission and reflection amplytudes of scattered electron in the field of one dimensional arbitrary potential is obtained. It is shown that in general the scattering…
We discuss the form of the propagator $U(t)$ for the time-dependent Schr\"odinger equation on an asyptotically Euclidean, or, more generally, asymptotically conic, manifold with no trapped geodesics. In the asymptotically Euclidean case, if…
In the context of quantum mechanics superoscillations, or the more general supershifts, appear as initial conditions of the time dependent Schr\"odinger equation. Already in \cite{ABCS21_2} a unified approach was developed, which yields…
We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
We present a classical integrable model of $SU(N)$ isospin defined on complex projective phase space in the external magnetic field and solve it exactly by constructing the action-angle variables for the system. We quantize the system using…
In this paper, we study the time-independent Schr\"odinger equation within the formalism of position dependent effective mass. For a generalized decomposition of the non-central effective potential, the deformed Schr\"odinger equation can…