Related papers: Zero-curvature solutions of the one-dimensional Sc…
An electron in quantum confinement takes on a discrete energy spectrum which is defined based on the solution to the Schrodinger Equation for a given potential. Well defined closed-form energy spectra are known for the particle in a box,…
We study Schr\"odinger operators on $L^2(E;m)$ of the form $-A+V$ with singular potentials $V$. We address the question posed by H. Brezis about the structure of the set $\{u=0\}$ for non-negative supersolutions to $-Au+Vu=0$. The class of…
We justify rigorously the convergence of the amplitude of solutions of Nonlinear-Schr\"odinger type Equations with non zero limit at infinity to an asymptotic regime governed by the Korteweg-de Vries equation in dimension 1 and the…
A new proposed one dimensional time independent Schr\"odinger equation is solved completely using shape invariance method. The corresponding potential is given by V_(x,A,B) =-A(sechpx)^2 - 6Bp(sech6px)^2+(tanhpx-6tanh6px)^2 with…
The algorithm for generation of exact solutions of the nonlinear equation in partial derivatives of a divergent type which is included in the formulation of magnetostatics, hydro-and aerodynamics, quantum mechanics (stationary Schr\"odinger…
An effective approach for solving the three-dimensional Dirac equation for spherically symmetric local interactions, which we have introduced recently, is reviewed and consolidated. The merit of the approach is in producing Schrodinger-like…
This paper discusses the use of the Riemann-Silberstein vector to solve the source-free Maxwell's equations and obtains novel analytical solutions. The solving process naturally leads to the spinor form of the source-free Maxwell's…
The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in the one-electron…
We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The…
Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. Coulomb-type potentials in these applications lead…
We consider the Dirac $\delta$-function potential problem in general case of deformed Heisenberg algebra leading to the minimal length. Exact bound and scattering solutions of the problem in quasiposition representation are presented. We…
The precise asymptotic behaviour of the solutions to the twodimensional curvature equation $\Delta u=k(z) e^{2 u}$ with $e^{2 u} \in L^1$ for bounded nonnegative curvature functions $-k(z)$ near isolated singularities is obtained.
In this work we investigate the quantum dynamics of an electric dipole in a $(2+1)$-dimensional conical spacetime. For specific conditions, the Schr\"odinger equation is solved and bound states are found with the energy spectrum and…
We are concerned with the half-space Dirichlet problem \[\begin{array}{ll} -\Delta v+v=|v|^{p-1}v & \textrm{in}\ \mathbb{R}^N_+, v=c\ \textrm{on}\ \partial\mathbb{R}^N_+, &\lim_{x_N\to \infty}v(x',x_N)=0\ \textrm{uniformly in}\…
We introduce the third five-parametric ordinary hypergeometric energy-independent quantum-mechanical potential, after the Eckart and P\"oschl-Teller potentials, which is proportional to an arbitrary variable parameter and has a shape that…
We study integrability by quadrature of a spatially flat Friedmann model containing both a minimally coupled scalar field $\phi$ with an exponential potential $V(\phi)\sim\exp[-\sqrt{6}\sigma\kappa\phi]$, $\kappa=\sqrt{8\pi G_N}$, of…
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…
For a quantum confinement model, the wave function of a particle is zero outside the confined region. Due to this, the negative energy states are, in fact, square integrable. As negative energy states are not physical, we need to impose…
Making an ansatz to the wave function, the exact solutions of the $D$% -dimensional radial Schrodinger equation with some molecular potentials like pseudoharmonic and modified Kratzer potentials are obtained. The restriction on the…
We consider the scattering problem for the nonlinear Schr\"{o}dinger equation with a potential in two space dimensions. Appropriate resolvent estimates are proved and applied to estimate the operator $A(s)$ appearing in commutator…