QUARTIC ANHARMONIC OSCILLATOR AND RANDOM MATRIX THEORY

Author:

CICUTA G.M.1,STRAMAGLIA S.2,USHVERIDZE A.G.3

Affiliation:

1. Dipartimento di Fisica, Universita di Parma, Viale delle Scienze, I-43100 Parma, Italy

2. Dipartimento di Fisica, Universita di Bari, Via Amendola 173, 70126 Bari, Italy

3. Department of Theoretical Physics, University of Lodz, Pomorska 149/153, 90–236 Lodz, Poland

Abstract

In this letter the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitian matrices is established. This relationship enables one to present several more or less closed expressions for the oscillator energy. One of such expressions is given in the form of simple recurrence relations derived by means of the method of orthogonal polynomials which is one of the basic tools in the theory of random matrices.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Physics and Astronomy,Astronomy and Astrophysics,Nuclear and High Energy Physics

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