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Title: On numerical solutions to the QCD ’t Hooft equation in the limit of large quark mass

First we give a short informal introduction to the theory behind the ’t Hooft equation. Then we consider numerical solutions to this equation in the limit of large fermion masses. It turns out that the spectrum of eigenvalues coincides with that of the Airy differential equation. Moreover when we take the Fourier transform of eigenfunctions, they look like the corresponding Airy functions with appropriate symmetry. It is known that these functions correspond to solutions of a one dimensional Schrodinger equation for a particle in a triangular potential well. So we find the analogy between this problem and the ’t Hooft equation. We also present a simple intuition behind these results.
Authors:
;  [1]
  1. Saint Petersburg State University, Saint Petersburg, Russia e-mail: roman.zubov@hep.phys.spbu.ru, evgeni.prokhvat@pobox.spbu.ru (Russian Federation)
Publication Date:
OSTI Identifier:
22499094
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1701; Journal Issue: 1; Conference: 11. conference on quark confinement and hadron spectrum, Saint Petersburg (Russian Federation), 8-12 Sep 2014; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AIRY FUNCTIONS; EIGENFUNCTIONS; EIGENVALUES; FOURIER TRANSFORMATION; MASS; NUMERICAL SOLUTION; ONE-DIMENSIONAL CALCULATIONS; PARTICLES; QUANTUM CHROMODYNAMICS; QUARKS; SCHROEDINGER EQUATION; SPECTRA