Heisenberg Evolution WKB and Symplectic Area Phases

Details Heisenberg Evolution WKB and Symplectic Area Phases Heisenberg Evolution WKB and Symplectic Area Phases

2002-01-08

arxiv.org/abs/quant-ph/0201029v1

J. Phys. A, 35:5279-5303, 2002

Physics

Quantum Physics

32 pages, 7 figures

Scientific paper

10.1088/0305-4470/35/25/309

The Schrodinger and Heisenberg evolution operators are represented in quantum phase space by their Weyl symbols. Their semiclassical approximations are constructed in the short and long time regimes. For both evolution problems, the WKB representation is purely geometrical: the amplitudes are functions of a Poisson bracket and the phase is the symplectic area of a region in phase space bounded by trajectories and chords. A unified approach to the Schrodinger and Heisenberg semiclassical evolutions is developed by introducing an extended phase space. In this setting Maslov's pseudodifferential operator version of WKB analysis applies and represents these two problems via a common higher dimensional Schrodinger evolution, but with different extended Hamiltonians. The evolution of a Lagrangian manifold in the extended phase space, defined by initial data, controls the phase, amplitude and caustic behavior. The symplectic area phases arise as a solution of a boundary condition problem. Various applications and examples are considered.

Affiliated with

Also associated with

No associations

Rating

Heisenberg Evolution WKB and Symplectic Area Phases does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Heisenberg Evolution WKB and Symplectic Area Phases, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Heisenberg Evolution WKB and Symplectic Area Phases will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-321951