Excited states configurations of the quantum Toda lattice

Excited states configurations of the quantum Toda lattice are studied by th r direct diagonalization of the Hamiltonian. The most probable configuratio ns of one-hole and one-particle excitations are shown to be similar to the profiles of classical phonon and soliton excitations, respectively. One-hol e excitation states, which are always ground states of definite E-m-symmetr y of the dihedral group D-N, change those structures abruptly with the pote ntial range varied. One-particle excitations, which are buried in complicat ed excitation spectra, have well-defined configurations similar to the cnoi dal profile of the classical periodic Toda lattice. The relationship that t he hole (particle) excitations in quantum mechanics correspond to the phono n (soliton) excitations in classical mechanics, which has been suggested ba sed on the similarity of dispersion relations, is confirmed in a geometrica lly understandable way. Based on the study of one-soliton and two-soliton s tates, the structure of multi-soliton states in quantum mechanics can be co njectured. (C) 2001 Academic Press.