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

arXiv:0707.3474 · Communications in Theoretical Physics

Groundstate with Zero Eigenvalue for Generalized Sombrero-Shaped Potential in N -Dimensional Space

Zhao Wei-Qin

Published Jul 1, 2008• 0 citations
arXivHTMLPDF

Abstract

Based on an iterative method for solving the groundstate of Schrödinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the parameters in the potential are discussed.
DOI
10.1088/0253-6102/50/1/30

Related papers

Iterative Solution for Generalized Sombrero-shaped Potential in $N$-dimensional Space

Wei‐Guang Zhao

An explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with generalized $N$-dimensional Sombrero-shaped potential is presented. The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameters are discussed.

arXiv:0712.4054•Dec 25, 2007•0 citations

Two kinds of iterative solutions for generalized sombrero-shaped potential inN-dimensional space

Zhao Wei-Qin

Based on two different iteration procedures the groundstate wavefunctions and energies for N -dimensional generalized Sombrero-shaped potentials are solved. Two kinds of trial functions for the iteration procedure are defined. The iterative solutions converge nicely on consistent results for different choices of iteration procedures and trial functions.

arXiv:0802.2606•Journal of Physics A Mathematical and Theoretical•May 15, 2008•0 citations

Convergent Iterative Solutions of Schroedinger Equation for a Generalized Double Well Potential ∗

Richard M. Friedberg, T. D. Lee, W. Q. Zhao

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with a generalized double well potential V = g2 2 (x2 − 1) 2 (x 2 + a). The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameter a are discussed.

•Jan 1, 2008•3 citations

General recursive solution for one dimensional quantum potentials

Sérgio Luiz Morelhão, André Perrotta

A revision of the recursive method proposed by S.A. Shakir [Am. J.Phys. \textbf{52}, 845 (1984)] to solve bound eigenvalues of the Schrodinger equation is presented. Equations are further simplified and generalized for computing wave functions of any given one-dimensional potential, providing accurate solutions not only for bound states but also for scattering and resonant states, as demonstrated here for a few examples.

arXiv:quant-ph/0605115•May 15, 2006•0 citations

Exact Solutions of Schrodinger Equation for a Ring-Shaped Potential

Özlem Yeşiltaş, R. Sever

The exact solutions of Schrodinger equation are obtained for a noncentral potential which is a ring-shaped potential. The energy eigenvalues and corresponding eigenfunctions are obtained for any angular momentum l. Nikiforov-Uvarov method is used in the computations.

arXiv:quant-ph/0703034•Mar 5, 2007•0 citations

The Scattering and Bound States of the Schrödinger Particle in Generalized Asymmetric Manning-Rosen Type Potential

Ahmet Taş, Soner Alpdoğan, Ali Havare

We solve exactly one-dimensional Schrödinger equation for the generalized asymmetric Manning-Rosen (GAMAR) type potential containing the different types of physical potential that have many application fields in the nonrelativistic quantum mechanics and obtain the solutions in terms of the Gauss hypergeometric functions. Then we determine the solutions for scattering and bound states. By using these states we calculate the reflection and transmission coefficients for scattering states and achieve a correlation that gives the energy eigenvalues for the bound states. In addition to these, we show how the transmission and reflection coefficients depend on the parameters which describe shape of the GAMAR type potential and compare our results with the results obtained in earlier studies.

Advances in High Energy Physics•Jan 1, 2014•3 citations
Iterative Solution for Generalized Sombrero-shaped Potential in NNN-dimensional Space
An explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with generalized NNN-dimensional Sombrero-shaped potential is presented. The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameters are discussed.
We solve exactly one-dimensional Schrödinger equation for the generalized asymmetric Manning-Rosen (GAMAR) type potential containing the different types of physical potential that have many application fields in the nonrelativistic quantum mechanics and obtain the solutions in terms of the Gauss hypergeometric functions. Then we determine the solutions for scattering and bound states. By using these states we calculate the reflection and transmission coefficients for scattering states and achieve a correlation that gives the energy eigenvalues for the bound states. In addition to these, we show how the transmission and reflection coefficients depend on the parameters which describe shape of the GAMAR type potential and compare our results with the results obtained in earlier studies.