Evolution of semiclassical quantum states in phase space
- 1 May 1979
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 12 (5) , 625-642
- https://doi.org/10.1088/0305-4470/12/5/012
Abstract
The authors derive a semiclassical formula for the Wigner function W(q,p,t) describing the evolution in the two-dimensional phase space qp of a nonstationary quantum state psi (q,t) for a system with one degree of freedom. The initial state psi (q,0) corresponds to a family of classical orbits represented by a curve C0 in qp. Under the classical motion C0 evolves into a curve Ct; it is shown that the region where W is large hugs Ct in an adiabatic fashion, and that W has semiclassical oscillations depending only on the geometry of Ct and neighbouring curves.Keywords
This publication has 14 references indexed in Scilit:
- Regular and irregular semiclassical wavefunctionsJournal of Physics A: General Physics, 1977
- Semi-classical mechanics in phase space: A study of Wigner’s functionPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1977
- Phase space interpretation of semiclassical theoryThe Journal of Chemical Physics, 1977
- Quantum oscillations in the semiclassical fermion μ-space densityAnnals of Physics, 1973
- Semiclassical approximations in wave mechanicsReports on Progress in Physics, 1972
- Corrected bohr-sommerfeld quantum conditions for nonseparable systemsAnnals of Physics, 1958
- Formulation of Quantum Mechanics Based on the Quasi-Probability Distribution Induced on Phase SpacePhysical Review B, 1958
- An extension of the method of steepest descentsMathematical Proceedings of the Cambridge Philosophical Society, 1957
- XXXI. The structure of an electromagnetic field in the neighbourhood of a cusp of a causticJournal of Computers in Education, 1946
- On the Connection Formulas and the Solutions of the Wave EquationPhysical Review B, 1937