Quartic Anharmonic Oscillator and Random Matrix Theory

Details Quartic Anharmonic Oscillator and Random Matrix Theory Quartic Anharmonic Oscillator and Random Matrix Theory

1995-10-11

arxiv.org/abs/hep-th/9510066v1

Mod.Phys.Lett. A11 (1996) 119-129

Physics

High Energy Physics

High Energy Physics - Theory

12 pages in Latex

Scientific paper

In this paper 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 hermitean 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.

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