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The Dirac equation is generalized to $D+1$ space-time.The conserved angular momentum operators and their quantum numbers are discussed. The eigenfunctions of the total angular momenta are calculated for both odd $D$ and even $D$ cases. The…

Atomic Physics · Physics 2009-11-07 Xiao-Yan Gu , Zhong-Qi Ma , Shi-Hai Dong

We present a novel numerical method and algorithm for the solution of the 3D axially symmetric time-dependent Schr\"odinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent…

Atomic Physics · Physics 2017-07-11 Szilárd Majorosi , Attila Czirják

The problem of confinement of spinless particles in 1+1 dimensions is approached with a linear potential by considering a mixing of Lorentz vector and scalar couplings. Analytical bound-states solutions are obtained when the scalar coupling…

High Energy Physics - Theory · Physics 2009-11-11 Antonio S. de Castro

Analytic solutions for the energy eigenvalues are obtained from a confined potentials of the form $br$ in 3 dimensions. The confinement is effected by linear term which is a very important part in Cornell potential. The analytic eigenvalues…

Quantum Physics · Physics 2020-10-22 Cheng-Qun Pang , Lei Huang , Duo-jie Jia , Tian-Jie Zhang

In this study, we solved Schr\"odinger equation with Cornell potential (Coulomb-plus-linear potential) by using neural network approach. Four different types of Cornell potential were used without a physical relevance. Besides that…

Computational Physics · Physics 2019-04-15 Halil Mutuk

Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator…

Mathematical Physics · Physics 2015-06-22 Richard L Hall , Nasser Saad

Exact solutions to the d-dimensional Schroedinger equation, d\geq 2, for Coulomb plus harmonic oscillator potentials V(r)=-a/r+br^2, b>0 and a\ne 0 are obtained. The potential V(r) is considered both in all space, and under the condition of…

Mathematical Physics · Physics 2015-05-30 Richard L. Hall , Nasser Saad , Kalidas Sen

A new approximation scheme to the centrifugal term is proposed to obtain the $l\neq 0$ bound-state solutions of the Schr\"{o}dinger equation for an exponential-type potential in the framework of the hypergeometric method. The corresponding…

Quantum Physics · Physics 2015-05-13 Sameer M. Ikhdair , Ramazan Sever

This work presents an alternative methodology for computing potentials matrix elements within the Lagrange-mesh method in momentum space. The proposed approach extends the range of treatable potentials to include previously inaccessible…

Quantum Physics · Physics 2026-02-27 Cyrille Chevalier , Joachim Viseur

The series solution of the radial part of the Schr\"odinger equation for simultaneous coulomb and harmonic potential involves three-term recursion relation and is thus difficult to solve for bound states. We have suggested a simple method…

Mathematical Physics · Physics 2013-08-12 Jishnu Goswami , Chandan Mondal , Dipankar Chakrabarti

The present contribution concerns the computation of energy eigenvalues of a perturbed anharmonic coulombic potential with irregular singularities using a combination of the Sinc collocation method and the double exponential transformation.…

Numerical Analysis · Mathematics 2019-01-04 M. Essaouini , B. Abouzaid , P. Gaudreau , H. Safouhi

By their very nature, field-theoretical Hamiltonians are derived in momentum representation. To solve the corresponding integro-differential equations is more difficult than to solve the simpler differential equations in configuration space…

High Energy Physics - Phenomenology · Physics 2007-05-23 S. Bielefeld , J. Ihmels , H. C. Pauli

By applying an ansatz to the eigenfunction, an exact closed form solution of the Schr\"{o}dinger equation in 2D is obtained with the potentials, $V(r)=ar^2+br^4+cr^6$, $V(r)=ar+br^2+cr^{-1}$ and $V(r)=ar^2+br^{-2}+cr^{-4}+dr^{-6}$,…

Quantum Physics · Physics 2007-05-23 Shi-Hai Dong

The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily…

Computational Physics · Physics 2015-05-14 William A. Karr , Christopher R. Jamell , Yogesh N. Joglekar

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…

Quantum Physics · Physics 2015-06-16 Amlan K. Roy

We apply the Frobenius method to the Schr\"{o}dinger equation with a truncated Coulomb potential. By means of the tree-term recurrence relation for the expansion coefficients we truncate the series and obtain exact eigenfunctions and…

Quantum Physics · Physics 2020-08-06 Francisco M. Fernández

A new method is presented for solving the momentum-space Schrodinger equation with a linear potential. The Lande-subtracted momentum space integral equation can be transformed into a matrix equation by the Nystrom method. The method…

High Energy Physics - Phenomenology · Physics 2009-11-07 Alfred Tang , John W. Norbury

Solving for the bound state eigenvalues of the Schr\"odinger equation is a tedious iterative process when the conventional shooting or matching method is used. In this work, we bypass the eigenvalue's dependence on the eigenfunction by…

Computational Physics · Physics 2019-01-31 Siu A. Chin , John Massey

This work is devoted to the study of some exactly solvable quantum problems of four, five and six bodies moving on the line. We solve completely the corresponding stationary Schr\"odinger equation for these systems confined in an harmonic…

Mathematical Physics · Physics 2015-01-20 A. Bachkhaznadji , M. Lassaut

Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic anharmonic oscillator and confining perturbed Coulomb models in…

Quantum Physics · Physics 2009-11-13 Sameer M. Ikhdair