An Entire Spectral Determinant for Semiclassical Quantization
نویسندگان
چکیده
We show that the eigenvalues of the first order partial differential equation derived by quasi-classical approximation of the Schrödinger 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.
منابع مشابه
Periodic Orbit Quantization beyond Semiclassics
A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher h̄ contributions to the spectral determinant. We apply the theory to billiard systems, and compare the periodic orbit quantization including the first h̄ contribution to the exact quantum mechanical results. Typeset using REVTEX
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