English
Related papers

Related papers: High-precision methods for Coulomb, linear confine…

200 papers

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…

Quantum Physics · Physics 2007-05-23 Petr A. Khomyakov

We consider the question of whether the high-energy eigenfunctions of certain Schr\"odinger operators on the $d$-dimensional hyperbolic space of constant curvature $-\kappa^2$ are flexible enough to approximate an arbitrary solution of the…

Spectral Theory · Mathematics 2022-02-07 Alberto Enciso , Alba García-Ruiz , Daniel Peralta-Salas

The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complimentary situations, firstly when the…

Nuclear Theory · Physics 2015-05-18 S L Yakovlev , M V Volkov , E Yarevsky , N Elander

In this study, we present analytical solutions of the Schr\"odinger equation with the Multiparameter potential containing the different types of physical potential via the asymptotic iteration method (AIM) by applying a Pekeris-type…

Quantum Physics · Physics 2017-02-02 Ahmet Taş , Ali Havare

The Schrodinger equation for stationary states in a central potential is studied in an arbitrary number of spatial dimensions, say q. After transformation into an equivalent equation, where the coefficient of the first derivative vanishes,…

Quantum Physics · Physics 2007-05-23 Giampiero Esposito

The Schrodinger equation with the PT-symmetric Hulthen potential is solved exactly by taking into account effect of the centrifugal barrier for any l-state. Eigenfunctions are obtained in terms of the Jacobi polynomials. The…

Quantum Physics · Physics 2007-09-10 Sameer M. Ikhdair , Ramazan Sever

The method of potential envelopes is used to analyse the bound-state spectrum of the Schroedinger Hamiltonian H = -Delta -v/(r+b), where v and b are positive. We established simple formulas yielding upper and lower energy bounds for all the…

Mathematical Physics · Physics 2009-11-07 Richard L. Hall , Qutaibeh D. Katatbeh

Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a ("hard-core amended") Coulomb potential in one dimension. We prove the existence of a…

High Energy Physics - Phenomenology · Physics 2009-10-31 Wolfgang Lucha , F. F. Schoberl

This work investigates the motion of a non-relativistic charged particle within the spacetime of a global monopole. We introduce the Schr\"odinger equation to describe the particle's motion with two interactions by considering the Kratzer…

This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the considered system (electron in the Coulomb potential in…

Mathematical Physics · Physics 2015-12-10 Veronika Gáliková , Samuel Kováčik , Peter Prešnajder

We use the Tridiagonal Representation Approach (TRA) to obtain exact scattering and bound states solutions of the Schr\"odinger equation for short-range inverse-square singular hyperbolic potentials. The solutions are series of square…

Quantum Physics · Physics 2019-02-01 A. D. Alhaidari

This paper presents the exact ground state solution for a diatomic particle system with position-dependent complex mass under action of a complex Morse potential in the quantum domain. By solving the position-dependent Schr\"odinger…

Quantum Physics · Physics 2025-12-24 Partha Sarathi , Bhaskar Singh Rawat

We investigate a method to solve a class of Schr{\"o}dinger equation eigenvalue problems numerically to very high precision $P$ (from thousands to a million of decimals). The memory requirement, and the number of high precision algebraic…

Mathematical Physics · Physics 2013-10-09 Asif Mushtaq , Amna Noreen , Kåre Olaussen , Ingjald Øverbø

Bound-state solutions of the singular harmonic oscillator and singular Coulomb potentials in arbitrary dimensions are generated in a simple way from the solutions of the one-dimensional generalized Morse potential. The nonsingular harmonic…

Quantum Physics · Physics 2016-05-04 Pedro H. F. Nogueira , Antonio S. de Castro

We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…

Mathematical Physics · Physics 2007-05-23 Omar Mustafa , Maen Odeh

We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a…

Mathematical Physics · Physics 2009-11-11 Hakan Ciftci , Richard L. Hall , Nasser Saad

Eigenfunctions of the Schrodinger equation with the Coulomb potential in the imaginary Lobachevsky space are studied in two coordinate systems admitting solutions in terms of hypergeometric functions. Normalization and coefficients of…

Mathematical Physics · Physics 2017-09-13 Yu. A. Kurochkin , V. S. Otchik , D. R. Petrosyan , G. S. Pogosyan

We present an analysis of the two-dimensional Schrodinger equation for two electrons interacting via Coulombic force and confined in an anizotropic harmonic potential. The separable case of wy = 2wx is studied particularly carefully. The…

Quantum Physics · Physics 2017-07-17 Przemyslaw Koscik , Anna Okopinska

In this work, we carefully study the energy eigen-values and splitting of heavy quarkonia as there exist $1/r^3$ and $\delta^3(\vec r)$ singular terms in the potential which make a direct numerical solution of the Schr\"{o}dinger equation…

High Energy Physics - Phenomenology · Physics 2018-01-17 Yi-Bing Ding , Xue-Qian Li , Peng-Nian Shen

The bound state energy eigenvalues for the two-dimensional Kepler problem are found to be degenerate. This "accidental" degeneracy is due to the existence of a two-dimensional analogue of the quantum-mechanical Runge-Lenz vector.…

Mathematical Physics · Physics 2009-11-07 D. G. W. Parfitt , M. E. Portnoi