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

Journal of Physics A Mathematical and General

The dipolar potential

DOMENICO PICCA

Published Sep 1, 1982• 3 citations
Publisher

Abstract

The analytical solution of the Schrodinger equation is presented in the case m=0 for the angular equation of the dipolar potential.
DOI
10.1088/0305-4470/15/9/029

Related papers

Analytical Solutions of the Schrodinger Equation for Hua Potential within the Framework of two Approximations Scheme

C. M. Ekpo, E. B. Ettah

In this paper, we solve analytically the Schrodinger equation for s-wave and arbitrary angular momenta with the Hua potential is investigated respectively. The wave function as well as energy equation are obtained in an exact analytical manner via the Nikiforov Uvarov method using two approximations scheme. Some special cases of this potentials are also studied.

arXiv:2012.11716•Dec 18, 2020•0 citations

Schrödinger equation with imaginary potential

Xiaozheng Ma, Costas M. Soukoulis

Physica B Condensed Matter•Feb 1, 2001•19 citations

Solution of the Schrödinger Equation in Spherical Coordinates

Elsevier eBooks•Jan 1, 2015•0 citations

Solutions of the Schrödinger equation for anisotropic dipole-dipole interaction plus van der Waals interaction

Ruijie Du, Ran Qi, Peng Zhang

By generalizing Gao's approach [] for solving the Schrödinger equation for an isotropic van der Waals (vdW) potential to the systems with a multiscale anisotropic long-range interaction, we derive the solutions for the Schrödinger equation for an anisotropic dipole-dipole interaction plus an isotropic attractive vdW potential, i.e., C d ( 1 − 3 cos 2 θ ) / r 3 − C 6 / r 6 , which is projected to the subspace with angular momentum l ≤ l cut , with l cut being an arbitrary angular-momentum cutoff. Here θ is the polar angle of the coordinate r and r = | r | . The asymptotic behaviors of these solutions for r → 0 and r → ∞ are obtained. The generalization of our approach for the case of an anisotropic vdW potential is also discussed. These results can be used in the research of collisions and chemical reactions between ultracold polar molecules in a static electric field. Our approach to derive the solutions can be applied to the systems with a general long-range potential ∑ λ = 2 λ max V λ ( θ , φ ) / r λ , with φ being the azimuthal angle of r , and thus can be used in collision problems between various kinds of molecules, ions, or atoms (e.g., the collisions between ultracold dipolar atoms).

arXiv:2207.09377•Physical Review Research•May 19, 2025•2 citations

Solutions of the Schrodinger Equation for Modified Mobius Square Potential using two Approximation Scheme

C. M. Ekpo, Jonathan Osang, E. B. Ettah

In this paper, the Schrodinger equation for s-wave and arbitrary angular momenta with the Modified Mobuis Square potential is investigated respectively. The eigenfunctions as well as energy eigenvalues are obtained in an exact analytical manner via the Nikiforov Uvarov method using two approximations scheme. Some special cases of this potentials are also studied.

arXiv:2012.11498•Dec 18, 2020•0 citations

Analytical solutions of the Schrodinger equation for finite harmonic-oscillator potential wells

Gintautas Kamuntavičius, Agnė Mašalaitė, Saulius Mickevičius

•Jan 1, 2009•0 citations
By generalizing Gao's approach [] for solving the Schrödinger equation for an isotropic van der Waals (vdW) potential to the systems with a multiscale anisotropic long-range interaction, we derive the solutions for the Schrödinger equation for an anisotropic dipole-dipole interaction plus an isotropic attractive vdW potential, i.e., C d ( 1 − 3 cos 2 θ ) / r 3 − C 6 / r 6 , which is projected to the subspace with angular momentum l ≤ l cut , with l cut being an arbitrary angular-momentum cutoff. Here θ is the polar angle of the coordinate r and r = | r | . The asymptotic behaviors of these solutions for r → 0 and r → ∞ are obtained. The generalization of our approach for the case of an anisotropic vdW potential is also discussed. These results can be used in the research of collisions and chemical reactions between ultracold polar molecules in a static electric field. Our approach to derive the solutions can be applied to the systems with a general long-range potential ∑ λ = 2 λ max V λ ( θ , φ ) / r λ , with φ being the azimuthal angle of r , and thus can be used in collision problems between various kinds of molecules, ions, or atoms (e.g., the collisions between ultracold dipolar atoms).