QUARTIC ANHARMONIC-OSCILLATOR AND RANDOM-MATRIX THEORY

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