The symbol of a function of an operator

Details The symbol of a function of an operator The symbol of a function of an operator

2004-11-08

arxiv.org/abs/math/0411163v2

Mathematics

Quantum Algebra

26 pages. v2 contains a better, shorter proof. The problem is considered in more generality. References are corrected

Scientific paper

We give an explicit formula for the symbol of a function of an operator.
Given an operator {\hat A} on L^2(R^N) with symbol A, and a function f, we
obtain the symbol of f(\hat A) in terms of A. As an application,
Bohr-Sommerfeld quantization rules are explicitely calculated at order 4 in
hbar.

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