A Mini-Review of the Kinetic Energy Partition Method in Quantum Mechanics-Reference-Cited by-同舟云学术

A Mini-Review of the Kinetic Energy Partition Method in Quantum Mechanics

Published:2024-03-01 Issue:3 Volume:16 Page:290
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Chen Yu-Hsin¹^ORCID,Wu I-Huan²,Chao Sheng D.²³^ORCID

Affiliation:

1. Department of Marine Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan

2. Institute of Applied Mechanics, National Taiwan University, Taipei 10617, Taiwan

3. Center for Quantum Science and Engineering, National Taiwan University, Taipei 10617, Taiwan

Abstract

Based on the idea of adiabatic symmetry, we present a novel basis set expansion method—the kinetic energy partition (KEP) method—for solving quantum eigenvalue problems. Broken symmetry is responsible for quantum entanglement in many-body systems via parametric non-adiabatic corrections. Starting from simple one-particle-in-one-dimension problems, we gradually increase the complexity in the number of particles and the interaction patterns. Our goal in the mini-review is to advocate for the utility of the KEP method in front-line research, in particular for research beginners in quantum many-body problems.

Funder

National Science and Technology Council of Taiwan

Publisher

MDPI AG

Link

https://www.mdpi.com/2073-8994/16/3/290/pdf

Reference27 articles.

1. Arteca, G.A., Fernández, F.M., Castro, E.A., Arteca, G.A., Fernández, F.M., and Castro, E.A. (1990). Large Order Perturbation Theory and Summation Methods in Quantum Mechanics, Springer.

2. P-wave Efimov physics implications at unitarity;Chen;Phys. Rev. A,2023

3. Spontaneous spatial symmetry breaking in two-component Bose-Einstein condensates;Esry;Phys. Rev. A,1999

4. Three and four identical fermions near the unitary limit;Higgins;Phys. Rev. A,2022

5. Andrews, D.L. (2021). Symmetry and quantum features in optical vortices. Symmetry, 13.