Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Russian Physics Journal

The wave functions and energy levels of a Schrödinger equation with the potential being the sum of a harmonic oscillator potential, a linear potential, and a Coulomb potential

N. V. Maksimenko, S. M. Kuchin

Published Dec 1, 2010• 2 citations
Publisher
DOI
10.1007/s11182-010-9484-0

Related papers

INFLUENCE OF EXTERNAL FIELDS ON THE KILLINGBECK POTENTIAL: QUASI EXACT SOLUTION

M. Hamzavi, Sameer M. Ikhdair

The Killingbeck potential consists of oscillator potential plus Cornell potential, i.e. ar2+ br - c/r, that it has received a great deal of attention in particle physics. In this paper, we study the energy levels and wave function for arbitrary m-state in two-dimensional (2D) Schrödinger equation (SE) with a Killingbeck potential under the influence of strong external uniform magnetic and Aharonov–Bohm (AB) flux fields perpendicular to the plane where the interacting particles are confined. We use the wave function ansatz method to solve the radial problem of the Schrödinger equation with Killingbeck potential. We obtain the energy levels in the absence of external fields and also find the energy levels of the familiar Coulomb and harmonic oscillator potentials.

Modern Physics Letters B•Sep 11, 2013•6 citations

Chapter 1 The wave function and Schrodinger equation

EDP Sciences eBooks•Apr 30, 2026•0 citations

The Schrödinger Equation in Potential Representation

WORLD SCIENTIFIC eBooks•Aug 1, 2020•0 citations

The Relation between Classical Mechanics and Wave Mechanics

Yoshio Nishiyama

Introducing a dimensional unit \hbar into classical mechanics, we make classical wave functions √ρ1exp (iS1/\hbar)-√ρ2exp (iS2/\hbar) for a one-particle system in the configuration space where √ρ1exp (iS1/\hbar) corresponds to the incident path (or one half) of an orbit and √ρ2exp (iS2/\hbar) to the outgoing (or another half), and ρ's and S's are densities and actions respectively. These classical wave functions are compared with the corresponding wave functions of solutions of the Schrödinger equation for three one-particle systems, the scattering by a Coulomb potential, the linear harmonic oscillator and an electron bound by a Coulomb potential. From the essential correspondence between them it is concluded that the Schrödinger wave function describes the steady, causal but a little imaginary motion of the one-particle system as √ρexp (iS/\hbar) in the configuration space where ρ is a density and S an action, and that the states which the wave equation describes exist continuously (not discrete) and the (discrete) stationary states are the ones where √ρexp (iS/\hbar) is uniquely determined throughout an orbit. The Dirac equation shows that an electron of optics (or the electromagnetic wave equation) can be considered as the Schrödinger (or Dirac) equation for the motion of a photon, a particle, in a potential. A quantum-electrodynamical wave equation which is composed of the Dirac equation with a Coulomb potential and the electromagnetic wave equation is constructed for the steady motion of a one-electron system without recource to the so-called second-quantization method. It gives finite energy shifts. A line shift is calculated: ΔE(2S1/2 →2P1/2) \cong709 Mc/s.

Progress of Theoretical Physics•Nov 1, 1963•1 citation

Non-Relativistic Particle under the Influence of Aharonov-Bohm Flux Field Subject to Physical Potentials and the Nikiforov-Uvarov Method

Faizuddin Ahmed, Kayser Ahmed, Akheruzzaman Ahmed +2 more

In this work, the non-relativistic wave equation via the Schrödinger wave equation under the influence of the Aharonov-Bohm flux field Subject to physical potentials of various kinds is investigated. These potentials are modified Coulomb potential, modified harmonic oscillator potential, the Kratzer-Feus potential, and the Mie-type potential which have wide applications in different branches of physics and chemistry. We solve the Schrodinger wave equation using the Nikiforov-Uvarov (NU) method and obtain the energy profiles and the wave function of the non-relativistic particle, and analyze the effects of potential and the quantum flux on them. We show that each non-relativistic energy level gets modified in comparison to the known results obtained in the literature.

arXiv:2208.04744•Aug 4, 2022•0 citations

Schrödinger Equation for Energy Levels as a Linear Equation for Probability Distributions Identified with Quantum States

Vladimir N. Chernega, Margarita A. Man’ko, Vladimir I. Man’ko

Journal of Russian Laser Research•Sep 1, 2020•6 citations
The Killingbeck potential consists of oscillator potential plus Cornell potential, i.e. ar2+ br - c/r, that it has received a great deal of attention in particle physics. In this paper, we study the energy levels and wave function for arbitrary m-state in two-dimensional (2D) Schrödinger equation (SE) with a Killingbeck potential under the influence of strong external uniform magnetic and Aharonov–Bohm (AB) flux fields perpendicular to the plane where the interacting particles are confined. We use the wave function ansatz method to solve the radial problem of the Schrödinger equation with Killingbeck potential. We obtain the energy levels in the absence of external fields and also find the energy levels of the familiar Coulomb and harmonic oscillator potentials.
Introducing a dimensional unit \hbar into classical mechanics, we make classical wave functions √ρ1exp (iS1/\hbar)-√ρ2exp (iS2/\hbar) for a one-particle system in the configuration space where √ρ1exp (iS1/\hbar) corresponds to the incident path (or one half) of an orbit and √ρ2exp (iS2/\hbar) to the outgoing (or another half), and ρ's and S's are densities and actions respectively. These classical wave functions are compared with the corresponding wave functions of solutions of the Schrödinger equation for three one-particle systems, the scattering by a Coulomb potential, the linear harmonic oscillator and an electron bound by a Coulomb potential. From the essential correspondence between them it is concluded that the Schrödinger wave function describes the steady, causal but a little imaginary motion of the one-particle system as √ρexp (iS/\hbar) in the configuration space where ρ is a density and S an action, and that the states which the wave equation describes exist continuously (not discrete) and the (discrete) stationary states are the ones where √ρexp (iS/\hbar) is uniquely determined throughout an orbit. The Dirac equation shows that an electron of optics (or the electromagnetic wave equation) can be considered as the Schrödinger (or Dirac) equation for the motion of a photon, a particle, in a potential. A quantum-electrodynamical wave equation which is composed of the Dirac equation with a Coulomb potential and the electromagnetic wave equation is constructed for the steady motion of a one-electron system without recource to the so-called second-quantization method. It gives finite energy shifts. A line shift is calculated: ΔE(2S1/2 →2P1/2) \cong709 Mc/s.
In this work, the non-relativistic wave equation via the Schrödinger wave equation under the influence of the Aharonov-Bohm flux field Subject to physical potentials of various kinds is investigated. These potentials are modified Coulomb potential, modified harmonic oscillator potential, the Kratzer-Feus potential, and the Mie-type potential which have wide applications in different branches of physics and chemistry. We solve the Schrodinger wave equation using the Nikiforov-Uvarov (NU) method and obtain the energy profiles and the wave function of the non-relativistic particle, and analyze the effects of potential and the quantum flux on them. We show that each non-relativistic energy level gets modified in comparison to the known results obtained in the literature.