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We consider radial solutions to the Schr\"odinger-Poisson system in three dimensions with an external smooth potential with Coulomb-like decay. Such a system can be viewed as a model for the interaction of dark matter with a bright matter…
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation…
We generalize the known solution of the Schr\"odinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the…
We discuss the explicit construction of the Schroedinger equations admitting a representation through some family of general polynomials. Almost all solvable quantum potentials are shown to be generated by this approach. Some generalization…
Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to…
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…
We discuss the construction of Maxwellian electrodynamics in 2+1 dimensions and some of its applications. Special emphasis is given to the problem of the retarded potentials and radiation, where substantial differences with respect to the…
We study two particles colliding in a $d$-dimensional finite volume and generalize L\"uscher's formula to arbitrary $d$ spatial dimensions. We obtain the $s$- and $p$-wave approximations of the generalized L\"uscher's formula. For resonant…
Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and…
We consider the ADM splitting of the Einstein-Hilbert action in five dimensions in the presence of matter that can be either a "point particle", or a set of scalar fields. The Hamiltonian, being a linear superposition of constraints, is…
In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…
We study the Schroedinger equation of a class of two-level systems under the action of a periodic time-dependent external field in the situation where the energy difference 2epsilon between the free energy levels is sufficiently small with…
This is a survey paper based on previous results of the author. In the paper, we define and discuss the generalizations of linear partial differential equations to multidimensional variational problems. We consider two examples of such…
A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.
We discuss solutions of the spherically symmetric wave equation and Klein Gordon equation in an arbitrary number of spatial and temporal dimensions. Starting from a given solution, we present various procedures to generate futher solutions…
The question of whether hydrogen atoms can exist or not in spaces with a number of dimensions greater than 3 is revisited, considering higher dimensional Euclidean spaces. Previous results which lead to different answers to this question…
The effective dynamics of solitons for the generalized nonlinear Schr\"odinger equation in a random potential is rigorously studied. It is shown that when the external potential varies slowly in space compared to the size of the soliton,…
A mapping between stationary solutions of nonlinear Sch\"odinger equations with real and complex potentials is constructed and a set of exact solutions with real energies are obtained for a large class of complex potentials. As specific…
Dirac, Schwinger and Zwanziger theories of electric and magnetic charges are obtained via duality transformation. Analogous construction for three Euclidean dimensions, with magnetic charges interacting with electric currents, is also done.…
The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb,…