there is a conjecture so called RIEMANN HYPOTHESIS , which have a deep relationship between the roots of the Riemann Zeta function and the eigenvalues of a Hamiltonian

http://arxiv.org/abs/1101.3116

http://findarticles.com/p/articles/mi_m1200/is_7_174/ai_n30887057/

and my humble paper about the subject http://vixra.org/pdf/1007.0005v8.pdf in fact RIEMANN HYPOTHESIS is juts to use WKB to find a Hamiltonian whose eigenvalues are the square of the RIemann zeros (imaginary part) and its FUNCTIONAL DETERMINANT is just the RIemann Xi function