Related papers: Equivalent power law potentials
The Schr\"odinger equation is solved for the wave function of an electron moving in a superposition of external constant and uniform electric and magnetic fields at an arbitrary angle between the field directions. The changing of the…
An attempt is made to describe the general-relativistic equations of motion for the Schwarzschild geometry in terms of the classical concepts of energy and angular momentum. Using the customary terms the geodesic equations can be viewed in…
The "potentials" being considered are analogues of classical Riesz potentials of order 1, and the idea is to look at how they might map L^p spaces into Sobolev spaces in various settings.
The variety of bi-confluent Heun potentials for a stationary relativistic wave equation for a spinless particle is presented. The physical potentials and energy spectrum of this wave equation are related to those for a corresponding…
New inverse and half-inverse problems: {\it sliding problems} are introduced. In this way several physically important equations are recovered from the quantum defect. In particular, sliding problems are solved for radial Schr\"odinger…
We investigate the Coulomb phase shift, and derive and analyze new and more precise analytical formulae. We consider next to leading order terms to the Stirling approximation, and show that they are important at small values of the angular…
Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
When the Schr\"{o}dinger equation for stationary states is studied for a system described by a central potential in $n$-dimensional Euclidean space, the radial part of stationary states is an even function of a parameter $\lambda$ which is…
A Schr\"odinger equation may be transformed by unitary operators into dynamical equations in different interaction pictures which share with it a common physical frame, i.e., the same underlying interactions, processes and dynamics. In…
A recently proposed algorithm to obtain global solutions of the double confluent Heun equation is applied to solve the quantum mechanical problem of finding the energies and wave functions of a particle bound in a potential sum of a…
A new approach has been used to evaluate the momentum and angular momentum of the isotropic and homogeneous cosmological models. It is shown that the results obtained for momentum exactly coincide with those already available in the…
We explore the spectral properties and behaviour of confining superexponential potentials. Several prototypes of these highly nonlinear potentials are analyzed in terms of the eigenvalues and eigenstates of the underlying stationary…
The relativistic bound-state energy spectrum and the wavefunctions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein-Gordon and Dirac equations are…
The self-similar potentials are formulated in terms of the shape-invariance. Based on it, a coherent state associated with the shape-invariant potentials is calculated in case of the self-similar potentials. It is shown that it reduces to…
We tried to determine the range of validity of a recently proposed modification of the Hellmann potential that leads to analytical eigenvalues and eigenfunctions. We discuss the difficulties that we found in the analysis of the main…
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz…
The Schr\"{o}dinger equation with the central potential is first studied in the arbitrary dimensional spaces and obtained an analogy of the two-dimensional Schr\"{o}dinger equation for the radial wave function through a simple…
An appropriateness of a space asymmetry of shape invariant potentials with scaling of parameters and potentials of Shabat and Spiridonov in calculation of their forms, wave functions and discrete energy spectra has proved and has…
We propose two generalisations of the Coulomb potential equation of quantum mechanics and investigate the occurence of algebraic eigenfunctions for the corresponding Scrh\"odinger equations. Some relativistic counterparts of these problems…