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

Acta Physica Sinica

Solution of radial equation of Kepler’s problem by pseudo-angular-momentum method and normalization of eigenstate and coherent state

Wenbo Li, Li Ke-Xuan, 北京交通大学物理系,北京 100044

Published Jan 1, 2004• 0 citations
Publisher

Abstract

By using the pseudoangularmomentum method, the radial equation for bound state of Kepler's problem is solved and the analytic expression for eigenstate is derived. The result shows that the normalization of eigenfunction that should be done carefully is quite peculiar. The corresponding coherent state is also discussed.
DOI
10.7498/aps.53.2964

Related papers

Coherent state of hydrogen-like atoms: an application of the pseudo-angular-momentum operator method

Wenbo Li, Li Mi-Shan, 北京交通大学物理系,北京 100044

Using the pseudo-angular-momentum operator method,the radial equation for bound state of the hydrogen-like atom is solved and the analytical expression for the eigenstate is derived. The result shows that the normalization of eigenfunction should be done carefully owing to its peculiarity. The corresponding coherent state is also discussed.

Acta Physica Sinica•Jan 1, 2008•0 citations

Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential

Felix Iacob, Marina Lute

We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.

arXiv:1411.5162•Journal of Mathematical Physics•Dec 1, 2015•15 citations

Coherent state of three-particle Calogero-Sutherland model

Wenbo Li, Li Mi-Shan, Yaling Li +5 more

The three-particle CSM (Calogero-Sutherland model) is solved by the pseudo-angular-momentum method. Analytic expressions of the eigenstate and coherent states are obtained.

Acta Physica Sinica•Jan 1, 2008•0 citations

Analytical bound-state solutions of the Schrödinger equation for the Manning–Rosen plus Hulthén potential within SUSY quantum mechanics

A. I. Ahmadov, Maria Naeem, M. V. Qocayeva +1 more

In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning–Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any [Formula: see text] angular momentum case via the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.

International Journal of Modern Physics A•Jan 30, 2018•23 citations

The number radial coherent states for the generalized MICZ-Kepler problem

M. Salazar-Ramírez, D. Ojeda-Guillén, R. D. Mota

We study the radial part of the McIntosh-Cisneros-Zwanziger (MICZ)-Kepler problem in an algebraic way by using the 𝔰𝔲(1, 1) Lie algebra. We obtain the energy spectrum and the eigenfunctions of this problem from the 𝔰𝔲(1, 1) theory of unitary representations and the tilting transformation to the stationary Schrödinger equation. We construct the physical Perelomov number coherent states for this problem and compute some expectation values. Also, we obtain the time evolution of these coherent states.

arXiv:1510.02841•Journal of Mathematical Physics•Feb 1, 2016•8 citations

Exact solutions of the radial Schrödinger equation for some physical potentials

Sameer Ikhdair, Ramazan Sever

Abstract By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrödinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained.

arXiv:quant-ph/0702141•Open Physics•Jan 1, 2007•49 citations
We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.
In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning–Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any [Formula: see text] angular momentum case via the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.
We study the radial part of the McIntosh-Cisneros-Zwanziger (MICZ)-Kepler problem in an algebraic way by using the 𝔰𝔲(1, 1) Lie algebra. We obtain the energy spectrum and the eigenfunctions of this problem from the 𝔰𝔲(1, 1) theory of unitary representations and the tilting transformation to the stationary Schrödinger equation. We construct the physical Perelomov number coherent states for this problem and compute some expectation values. Also, we obtain the time evolution of these coherent states.