Related papers: Some non-relativistic implications of hydrogenic s…
General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed…
A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we…
A two-dimensional hydrogen atom offers a promising alternative for describing the quantum interaction between an electron and a proton in the presence of a straight cosmic string. Reducing the hydrogen atom to two dimensions enhances its…
The nonrelativistic hydrogen atom in $D=3-2\epsilon$ dimensions is the reference system for perturbative schemes used in dimensionally regularized nonrelativistic effective field theories to describe hydrogen-like atoms. Solutions to the…
Analytical approximations are constructed for binding energies, quantum-mechanical sizes and oscillator strengths of main radiative transitions of hydrogen atoms arbitrarily moving in magnetic fields 10^{12}-10^{13} G. Examples of using the…
The aim of this article is to study a nonlinear system modeling a Non-Newtonian fluid of polymer aqueous solutions. We are interested here in the existence of weak solutions for the stationary problem in a bounded plane domain or in…
A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…
In this paper we analyze a recently proposed approach for the construction of antisymmetric functions for atomic and molecular systems. It is based on the assumption that the main problems with Hartree-Fock wavefunctions stem from their…
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 invariant mass of free particles is used to derive a bound-state equation for the hydrogen atom at rest. This equation has the well-known solutions for the single-particle states. Existence of two-particle bound states, for which the…
We have obtained the uncertainty relations for arbitrary states of the hydrogen atom. It is shown that the minimal value of the uncertainty relation is attained for the circular Rydberg states.
Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
We present examples of simple electromagnetic systems in which energy, linear momentum, and angular momentum exhibit interesting behavior. The systems are sufficiently simple to allow exact solutions of Maxwell's equations in conjunction…
A novel method for the exact solvability of quantum systems is discussed and used to obtain closed analytical expressions in arbitrary dimensions for the exact solutions of the hydrogenic atom in the external potential $\Delta…
Since molecular energy transformations are responsible for chemical reaction rates at the most fundamental level, chemical kinetics should provide some information about molecular energies. This is the premise and objective of this note. We…
It is shown that the Schr\"{o}dinger equation for a system of interacting particles whose Compton wavelengths are of the same order of magnitude as the system size is contradictory and is not strictly nonrelativistic, because it is based on…
The Rydberg formula along with the Ritz quantum defect ansatz has been a standard theoretical tool used in atomic physics since before the advent of quantum mechanics, yet this approach has remained limited by its non-relativistic…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
Monogenic functions in the algebra of 5-dimensional spacetime have been used previously by the author as first principle in different areas of fundamental physics; the paper recovers that principle applying it to the hydrogen atom. The…