Related papers: Relativistic Wave Equations: An Operational Approa…
Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also…
The eigenvalue problem for one-dimensional Schr\"{o}dinger equation with the rational potential is numerically solved by the operator method. We show that the operator method, applied for solving the Schr\"{o}dinger equation with the…
A nonrelativistic equation for the system of two interacting particles within the framework of a model with noncommuting operators of coordinates and momenta of different particles is proposed, and a self-consistent system of equations for…
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…
Dirac-Coulomb type differential equation and its solution relativistic exponential-type spinor orbitals are introduced. They provide a revised form for operator invariants, namely Dirac invariants, simplifying the treatment of the angular…
A class of non-linear eigenvalue problems defined in the form of operator polynomials is investigated. The problems are related to wave equations which appear in a relativistic quantum field theory. Spectral asymptotics for this class are…
By the method of discrete transformation equations of 3-th wave hierarchy are constructed. The main difference compare with the systems connected with $A_1$ algebra consists in a fact that in $A_2$ case there are two different systems of…
We present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates. As an application we analyse linear stability of the fundamental self--similar solution of the wave equation with a focusing…
The Dirac equation plays an essential role in the relativistic quantum systems, which is reduced to a form similar to Schrodinger equation when a certain potential's type is selected as the Cornell potential. By choosing the generalized…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…
In the last years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised. On one side, "direct" quantum algorithms that aim at encoding the solution of the PDE by executing one…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the…
The relativistic wave equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave, in a medium of index of refraction n_m < 1, have been studied. In the Dirac case the found exact solutions…
A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free…
The solution of the Schrodinger equation with a linear potential is considered. We use algebraic methods to obtain the explicit form of the solution for the explicitly time dependent Hamiltonian and discuss the general conditions which…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
The relativistic quantum mechanics of two interacting particles is considered. We first present a covariant formulation of kinematics and of reduced phase space, giving a short outline of the classical results. We then quantize the systems…
We initiate a mathematically rigorous study of Klein-Gordon position operators in single-particle relativistic quantum mechanics. Although not self-adjoint, these operators have real spectrum and enjoy a limited form of spectral…