Semiclassical structure of Hamiltonians Academic Article uri icon

abstract

  • The structure of few-body Hamiltonian matrices is studied in thesemiclassical regime. Given(/ital A/cflx ///sub 1/(/bold q/cflx //,/bold p/cflx //),/ital A/cflx ///sub 2/(/bold q/cflx //,/bold p/cflx //)), a pair of operators,it can be shown that, underquite general conditions, /ital A/cflx ///sub 2/ takes the form of a banded matrixin the ordered eigenrepresentation of /ital A/cflx ///sub 1/. Moreover, thebandwidth depends only on /h bar/ and certain generalized microcanonicalaverages. In particular, if /ital H/=/ital H//sub 0/+epsilonV, this implies that theperturbed Hamiltonian is banded in the appropriately ordered unperturbed basis.

publication date

  • January 1, 1989