Ground state of the quantum periodic Toda lattice in the large-N limit

In Gutzwiller's formulation of the quantum periodic Toda lattice, quantization conditions are expressed in terms of Floquet's characteristic exponents which are equal to the zeros of a Hill-type determinant. We have derived an integral equation for the density distribution of those zeros for the ground state in the large-N limit. The large-N asymptotic expansions of the conserved quantities given by this density distribution are found to be fairly good approximations to the exact values. We have also carried out the semiclassical quantization by the EBK formulation and the semiclassical eigenvalues turned out to be very close to the exact values. (author)