Eur. Phys. J. Plus (2021) 136: 374
https://doi.org/10.1140/epjp/s13360-021-01342-x

Regular Article

Many-body quantum system in the presence of solvable potential

Physics Department, Shahed University, Tehran, Iran

^a z.bakhshi@shahed.ac.ir

Received: 13 May 2020
Accepted: 23 March 2021
Published online: 8 April 2021

Abstract

This article introduces a four-particle quantum system presented with a discrete energy spectrum, including harmonic potential and three-body interaction potential. By defining each particle’s Jacobi coordinates separately, one coordinate is eliminated as a transition in the energy spectrum. Then, the system is studied in polar coordinates, and by using the variables separation method, the Schrödinger equation of the system is transformed into three separate differential equations. Therefore, energy eigenvalues and wave eigenfunctions are calculated in each dimension. Additionally, the wave eigenfunctions figures are investigated in one and three dimensions. Then, we consider this quantum model with N particles in one dimension, and energy eigenvalues and wave eigenfunctions are obtained in ground and evoked states.