AN ENTIRE SPECTRAL DETERMINANT FOR SEMICLASSICAL QUANTIZATION

Abstract

We show that the eigenvalues of the first order partial differential equation derived by quasi-classical approximation of the Schrodinger equation can be computed from the trace of a classical operator. The derived trace formula is different from the Gutzwiller trace formula. The Fredholm determinant of the new operator is an entire function of the complex energy plane in contrast to the semi-classical spectral determinant derived from the Gutzwiller trace formula.