Some Remarks About Semiclassical Trace Invariants and Quantum Normal Forms
arXiv:0901.2994 · doi:10.1007/s00220-009-0920-3
Abstract
In this paper we explore the connection between semi-classical and quantum Birkhoff canonical forms (BCF) for Schrodinger operators. In particular we give a "non-symbolic" operator theoretic derivation of the quantum Birkhoff canonical form and provide an explicit recipe for expressing the quantum BCF in terms of the semi-classical BCF.