Quantum Surface of Section Method: Decomposition of the Resolvent (E - H)^(-1)

Details Quantum Surface of Section Method: Decomposition of the Resolvent (E - H)^(-1) Quantum Surface of Section Method: Decomposition of the Resolvent (E - H)^(-1)

1995-02-08

arxiv.org/abs/chao-dyn/9502008v1

Nonlinear Sciences

Chaotic Dynamics

20 pages, 1 figure, file in plain LaTeX includes the figure

Scientific paper

The paper presents exact surface of section reduction of quantum mechanics. The main theoretical result is a decomposition of the energy-dependent propagator G(E) = (E - H)^(-1) in terms of the propagators which (also or exclusively) act in Hilbert space of complex-valued functions over the configurational surface of section, which has one dimension less than the original configuration space. These energy-dependent quantum propagators from and/or onto the configurational surface of section can be explicitly constructed as the solutions of the first order nonlinear Riccati-like initial value problems.

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