Abstract

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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.