Many-body quantum system in the presence of solvable potential

Zahra Bakhshi | Sare Khoshdooni

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=158489
Date :  2021/04/08
Publish in :    The European Physical Journal Plus
DOI :  https://doi.org/10.1140/epjp/s13360-021-01342-x
Link :  http://dx.doi.org/10.1140/epjp/s13360-021-01342-x
Keywords :Many-body quantum system, solvable potential

Abstract :

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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.