Semiclassical structure of Hamiltonians
- 1 June 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 39 (12), 6507-6514
- https://doi.org/10.1103/physreva.39.6507
Abstract
The structure of few-body Hamiltonian matrices is studied in the semiclassical regime. Given (A(q^,p^),A (q^,p^)), a pair of operators, it can be shown that, under quite general conditions, A takes the form of a banded matrix in the ordered eigenrepresentation of A. Moreover, the bandwidth depends only on ħ and certain generalized microcanonical averages. In particular, if H=+εV, this implies that the perturbed Hamiltonian is banded in the appropriately ordered unperturbed basis.
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