QUANTIZING THE TODA LATTICE

In this work we study the quantum Toda lattice, developing the asympto tic Bethe ansatz method first used by Sutherland. Despite its known li mitations we find, on comparing with Gutzwiller's exact method, that i t works well in this particular problem and in fact becomes exact as ( h) over bar grows large. We calculate ground state and excitation ener gies for finite-sized lattices, identify excitations as phonons and so litons on the basis of their quantum numbers, and find their dispersio ns. These are similar to the classical dispersions for small (h) over bar, and remain similar all the way up to (h) over bar = 1, but then d eviate substantially as we go farther into the quantum regime. On comp aring the sound velocities for various (h) over bar obtained thus with that predicted by conformal theory we conclude that the Bethe ansatz gives the energies per particle accurate to O(1/N-2). On that assumpti on we can find correlation functions. Thus the Bethe ansatz method can be used to yield much more than the thermodynamic properties which pr evious authors have calculated.