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

Springer eBooks

Variational Method Applied to Schrödinger-Like Equation

Elso Drigo Filho, Regina Maria Ricotta, Natália Fávaro Ribeiro

Published Jan 1, 2019• 0 citations
Publisher
DOI
10.1007/978-3-030-20087-9_12

Related papers

Scaling, generator coordinate method and the eigensolutions of the Schrodinger equation

Carlos Esebbag, J Nunez, Angel Ricardo Plastino +1 more

An extremely simple (approximate) variational method for the study of the eigensolutions of the one-dimensional Schrodinger equation is introduced, based upon the idea of employing scaled eigenstates of the harmonic oscillator as generating functions for the generator coordinate method. The approach is successfully applied to a variety of situations.

Journal of Physics A Mathematical and General•Dec 21, 1985•3 citations

Variational solution of the Schrödinger equation

Kálmán Varga, Joseph A. Driscoll

Cambridge University Press eBooks•Apr 14, 2011•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

Simple variational approach to the one-dimensional Schrodinger equation

Guillermo H. Bozzolo, Angel Ricardo Plastino

Kinam•Jan 1, 1981•1 citation

A Variational Approach to Large Amplitude Collective Motions

M. Iwasaki

Large amplitude collective motions in a many-Fermion system are discussed from a standpoint of the variational method. In our method, the variational space itself is also determined by a variational procedure which is an extension of the Peierls-Yoccoz method. The Schrödinger equation for large amplitude collective motions is obtained under the additional approximations: ( i ) The variational space forms a Lie group and ( ii ) it is separated adiabatically from the remaining space. Our method may be regarded as the Born-Oppenheimer approximation in the unclear physics. Finally it is applied to the Lipkin model.

Progress of Theoretical Physics•Dec 1, 1983•0 citations

VARIATIONAL METHODS IN QUANTUM MECHANICS

Béla Gazdy

Periodica Polytechnica Mechanical Engineering•Jan 1, 1977•6 citations
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.
Large amplitude collective motions in a many-Fermion system are discussed from a standpoint of the variational method. In our method, the variational space itself is also determined by a variational procedure which is an extension of the Peierls-Yoccoz method. The Schrödinger equation for large amplitude collective motions is obtained under the additional approximations: ( i ) The variational space forms a Lie group and ( ii ) it is separated adiabatically from the remaining space. Our method may be regarded as the Born-Oppenheimer approximation in the unclear physics. Finally it is applied to the Lipkin model.