Related papers: Generalized quantum mechanical two Coulomb centers…
We present a precise fully relativistic numerical solution of the two-center Coulomb problem. The special case of unit nuclear charges is relevant for the accurate description of the ${\rm H}_2^+$ molecular ion and its isotopologues,…
Planar supersymmetric quantum mechanical systems with separable spectral problem in curvilinear coordinates are analyzed in full generality. We explicitly construct the supersymmetric extension of the Euler/Pauli Hamiltonian describing the…
In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild-like metric. As a test, the hydrogen atom…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
In this paper, we investigate the Schr\"odinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all…
Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schr\"{o}dinger equation is applied for a solution of a two--dimensional (2D) problem for two particles interacting via Kratzer,…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem of the radial Shrodinger equation with the screened Coulomb potential is developed. Based upon h-expansions and new quantization…
We discussed exact solutions of the Schroedinger equation for a two-dimensional parabolic confinement potential in a homogeneous external magnetic field. It turns out that the two-electron system is exactly solvable in the sense, that the…
We present a multiscale quantum-defect theory based on the first analytic solution for a two-scale long range potential consisting of a Coulomb potential and a polarization potential. In its application to atomic structure, the theory…
We present a procedure to solve the Schroedinger equation of two interacting electrons in a quantum dot in the presence of an external magnetic field within the context of quasi-exactly-solvable spectral problems. We show that the…
We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using…
A set of quasi-exactly solvable quantum mechanical potentials associated with the Poeschl-Teller potential, the generalized Poeschl-Teller potential, the Scarf potential, and the harmonic oscillator potential have been studied. Solutions of…
The Coulomb problem for Schr\"{o}dinger equation is examined, in spaces of constant curvature, Lobachevsky H_{3} and Riemann S_{3} models, on the base of generalized parabolic coordinates. In contrast to the hyperbolic case, in spherical…
We analyze two conditionally solvable quantum-mechanical models: a one-dimensional sextic oscillator and a perturbed Coulomb problem. Both lead to a three-term recurrence relation for the expansion coefficients. We show diagrams of the…
We present a separable expansion approximation method for Coulomb-like potentials which is based on Schwinger variational principle and uses Coulomb-Sturmian functions as basis states. The new scheme provides faster convergence with respect…
We explore the quantum Coulomb problem for two-body bound states, in $D=3$ and $D=3-2\epsilon$ dimensions, in detail, and give an extensive list of expectation values that arise in the evaluation of QED corrections to bound state energies.…
We demonstrate that the Schr\"odinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational…
It is shown that the two-body Coulomb problem in the Sturm representation leads to a new two-dimensional, exactly-solvable, superintegrable quantum system in curved space with a $g^{(2)}$ hidden algebra and a cubic polynomial algebra of…
We propose a simple quantum mechanical equation for $n$ particles in two dimensions, each particle carrying electric charge and magnetic flux. Such particles appear in (2+1)-dimensional Chern-Simons field theories as charged vortex soliton…
The paper studies the quantum mechanical Coulomb problem on a 3-sphere. We present a special parametrization of the ellipto-spheroidal coordinate system suitable for the separation of variables. After quantization we get the explicit form…