Classical periodic orbits and quantum mechanical eigenvalues and eigenfunctions

Details Classical periodic orbits and quantum mechanical eigenvalues and eigenfunctions Classical periodic orbits and quantum mechanical eigenvalues and eigenfunctions

May 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..56..325c&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 56, no. 1-2, p. 325-336.

Astronomy and Astrophysics

Astronomy

Eigenvalues, Hamiltonian Functions, Orbital Resonances (Celestial Mechanics), Orbits, Poincare Problem, Quantum Mechanics, Autocorrelation, Degrees Of Freedom, Schroedinger Equation

Scientific paper

We have calculated several families of classical periodic orbits in simple Hamiltonian systems of two degrees of freedom and the corresponding quantum mechanical eigenvalues and eigenfunctions. We have found that in most cases the eigenfunctions have their maxima and minima on some simple periodic orbits. These periodic orbits are of several resonant types and can be either stable or unstable. In the latter case the quantum Poincare surfaces of section are very different from the classical Poincare surfaces of section.

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