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

理论物理通讯:英文版

Revised Iterative Solution of Ground State of Double-Well Potential

ZHAOWei-Qin

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The revised new iterative method for solving the ground state of Schrodinger equation is deduced. Based on Green functions defined by quadratures along a single trajectory this iterative method is applied to solve the ground state of the double-well potential. The result is compared to the one based on the original iterative method. The limitation of the asymptotic expansion is also discussed.

Related papers

Revised Iterative Solution of Ground State of Double-Well Potential

Zhao Wei-Qin

The revised new iterative method for solving the ground state of Schrödinger equation is deduced. Based on Green functions defined by quadratures along a single trajectory this iterative method is applied to solve the ground state of the double-well potential. The result is compared to the one based on the original iterative method. The limitation of the asymptotic expansion is also discussed.

arXiv:quant-ph/0408055•Communications in Theoretical Physics•Jun 1, 2005•2 citations

Variational-Iterative Solution of Ground State for Central Potential

Zhao, Wei-Qin

The newly developed iterative method based on Green function defined by quadratures along a single trajectory is combined with the variational method to solve the ground state quantum wave function for central potentials.As an example, the method is applied to discuss the ground state solution of Yukawa potential, using Hulthen solution as the trial function.

理论物理通讯:英文版•Jan 1, 2002•0 citations

Wronskian Approach and the One-dimensional Schrodinger Equation with Double-well Potential

Qiu Jian, Ru-keng Su C

A Wronskian determinant approach is suggested to study the energy and the wave function for one-dimensional Schrodinger equation. An integral equation and the corresponding Green's function are constructed. As an example, we employed this approach to study the problem of double-well potential with strong coupling. A series expansion of ground state energy up to the second order approximation of iterative procedure is given.

arXiv:quant-ph/0209111•Sep 20, 2002•0 citations

Wronskian Approach and One-Dimensional Schrödinger Equation with Double-Well Potential

Qiu Jian, Su Rukeng

A Wronskian determinant approach is suggested to study the energy and the wave function for one-dimensional Schrodinger equation. An integral equation and its corresponding Green function are constructed. As an example, we employed this approach to study the problem of double-well potential with strong coupling. A series of expansion of ground state energy up to the second order approximation of iterative procedure is given.

Communications in Theoretical Physics•Jan 15, 2003•0 citations

Wronskian Approach and One—Dimensional Schroedinger Equation with Double—Well Potential

QIUJian, SURu-Keng

A Wronskian Determinant approach is suggested to study the energy and the wave function for onedimensional Schroedinger equation.An integral equation and its corresponding Green function are constructed.As an example,we employed this approach to study the problem of double-well potential with strong coupling,A series of expansion of ground state energy up to the second order approximation of iterative procedure is given.

理论物理通讯:英文版•Jan 1, 2003•0 citations

Solving Two-Dimensional Schrödinger Equation for a Double Well Potential Using Analytical and Variational Methods

Kathryn Chain, Dylan Herrmann, Julio Navas

The Schrödinger equation serves as a pivotal differential equation, capturing the fundamental duality of particles as both matter and waves. Upon solving it, we derive a particle's wave function within a given potential, delineating the confines within which the particle operates. This wave function enables us to ascertain the "most probable" values for parameters such as position, momentum, and energy within the specified potential. In this study, we focus on the double-well potential in two dimensions, resembling a bowl-like structure. Specifically tailored equations, termed Equation 1 and Equation 2, stem from the general Schrödinger equation when applied to the prescribed conditions. This research aims to utilize these equations to describe a particle’s behavior within the ground and the first excited states of the double well potential, employing two distinct methodologies. The first methodology involves leveraging the variational method on Equations 1 and 2 to obtain approximate solutions, providing crucial inputs for our subsequent approach. The second methodology serves as entails an analytical solution of Equations 1 and 2. A comparative analysis of the outcomes from both methods is anticipated to ensure the coherence and validity of the variational method. This project integrates key principles and proficiencies from both physics and mathematics disciplines, offering a platform for honing practical skills in applying these methodologies within a real-world context.

•Mar 22, 2024•0 citations
The revised new iterative method for solving the ground state of Schrodinger equation is deduced. Based on Green functions defined by quadratures along a single trajectory this iterative method is applied to solve the ground state of the double-well potential. The result is compared to the one based on the original iterative method. The limitation of the asymptotic expansion is also discussed.
The Schrödinger equation serves as a pivotal differential equation, capturing the fundamental duality of particles as both matter and waves. Upon solving it, we derive a particle's wave function within a given potential, delineating the confines within which the particle operates. This wave function enables us to ascertain the "most probable" values for parameters such as position, momentum, and energy within the specified potential. In this study, we focus on the double-well potential in two dimensions, resembling a bowl-like structure. Specifically tailored equations, termed Equation 1 and Equation 2, stem from the general Schrödinger equation when applied to the prescribed conditions. This research aims to utilize these equations to describe a particle’s behavior within the ground and the first excited states of the double well potential, employing two distinct methodologies. The first methodology involves leveraging the variational method on Equations 1 and 2 to obtain approximate solutions, providing crucial inputs for our subsequent approach. The second methodology serves as entails an analytical solution of Equations 1 and 2. A comparative analysis of the outcomes from both methods is anticipated to ensure the coherence and validity of the variational method. This project integrates key principles and proficiencies from both physics and mathematics disciplines, offering a platform for honing practical skills in applying these methodologies within a real-world context.