Classical and quantum mechanical systems of Toda-lattice type

Solutions to the classical periodic and non-periodic Toda lattice type Hamiltonian systems are expressed in terms of an Iwasawa-type factorization of a large Lie group. The scattering of these systems is determined in the non-periodic case. For the generalized periodic Toda lattices a generalization of Kostant's formula is obtained using standard representations of affine Lie groups.Research partially supported by NSF Grant MCS 83-01582Research partially supported by NSF Grant MCS 79-03153