Abstract
We investigate the classical and quantum dynamics of a particle trapped in a gravitational confocal parabolic billiard. Characterizing the equi-momentum surfaces and the Poincaré phase maps reveals four different kinds of motion the particle can exhibit. The analytical expressions of the characteristic equations for getting periodic orbits and their periods were derived and validated numerically. A notable finding is the possibility of having degenerate periodic trajectories with the same energy but different second constants of motion and caustics. Eigenstates of the particle with definite values of the constants of motion can be associated with classical orbits with the same pair of constants. To make this correspondence we use periodic orbits.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Communications in Nonlinear Science and Numerical Simulation
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
