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

Journal Article · Fri Jan 22 00:00:00 EST 2016 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4938710· OSTI ID:22499094

Zubov, Roman; Prokhvatilov, Evgeni ^[1]

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1. Saint Petersburg State University, Saint Petersburg, Russia e-mail: [e-mail], [e-mail] (Russian Federation)

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.

• OSTI ID: 22499094
• Journal Information: AIP Conference Proceedings, Vol. 1701, 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); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

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