相关论文: Charged particle in the field an electric quadrupo…

Here I show that a classical or quantum bit state plus one simple operation, an action, are sufficient ingredients to derive a quantum dynamical equation that rules the sequential changes of the state. Then, by assuming that a freely moving…

This is the fourth article in a series where we succeed in enlarging the class of exactly solvable quantum systems. We do that by working in a complete set of square integrable basis that carries a tridiagonal matrix representation for the…

We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles, relaxing an unnecessary assumption on the structure of the four-potential inherent to the standard approach and thus restoring the full…

Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…

In this paper it is shown that the equations of electric field lines of an arbitrarily moving charged particle in the general case are reduced to homogeneous, linear differential equations with variable coefficients. For trajectories where…

The energy spectrum of a nonrelativistic particle on a noncommutative sphere in the presence of a magnetic monopole field is calculated. The system is treated in the field theory language, in which the one-particle sector of a charged…

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…

Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…

We present a very efficient technique for solving the three-dimensional time-dependent Schrodinger equation. Our method is applicable to a wide range of problems where a fullly three-dimensional solution is required, i.e., to cases where no…

The time independent Schoedinger equation for two electrons confined in a parabolic external potential is solved. Developing this solution in terms of a dimensionless variable it is demonstrated that parameterization of the strength of the…

In this paper we obtain the expression for the self-force in the model with the Lagrangian containing additional terms, quadratic in Maxwell tensor derivatives (so-called Bopp-Podolsky electrodynamics). Features of this force are analyzed…

Analytical solutions to the time-dependent Shr\"{o}dinger equation in one dimension are developed for time-independent potentials, one consisting of an infinite wall and a repulsive delta function. An exact solution is obtained by means of…

A duality between an electrostatic problem in a three dimensional world and a quantum mechanical problem in a one dimensional world which allows one to obtain the ground state solution of the Schr\"odinger equation by using electrostatic…

Fully numerical mesh solutions of 2D and 3D quantum equations of Schroedinger and Hartree-Fock type allow us to work with wavefunctions which possess a very flexible geometry. This flexibility is especially important for calculations of…

We show that for non-relativistic free particles, the (bosonic) many particle equations can be rewritten in geometric fashion in terms of a classical theory of conformally stretched spacetime. We further generalize the results for the…

We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…

We find the Noether point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries are composed of a quasi-invariance transformation, a time-dependent rotation and a time-dependent spatial translation. The…

We consider a charged particle which is driven by a time-dependent flux threading a circular ring system. Various approaches including classical treatment, Fourier expansion method, time-evolution method, and Lewis-Riesenfeld method are…

We set up the classical wave equation for a particle formed of an oscillatory zero-rest-mass charge together with its resulting electromagnetic waves, traveling in a potential field $V$ in a susceptible vacuum. The waves are…

Solutions of time-independent Schrodinger equation for potentials periodic in space satisfy Bloch theorem. The theorem has been used to obtain solutions of the Schrodinger equation for periodic systems by expanding them in terms of plane…