Transformation of the Kepler problem
Abstract
The connection between the Kepler problem and the oscillator is examined both in classical and quantum mechanics, and transformations that map bound orbits of the Kepler problem in two and three dimensions to oscillator orbits are derived. The classical transformations are canonical and act in the extended phase space of the system. The transformation that maps the three dimensional Kepler problem provides an alternative to the KustaanheimoStiefel transformation. From it a transformation of space and time coordinates that maps the Hamilton Jacobi equation of the three dimensional Kepler problem to that of the oscillator is derived. The corresponding quantum transformations of Hilbert spaces are written in terms of the generating functions of the classical transformations. Quasiclassical states of the Kepler problem are constructed by transforming oscillator coherent states, and the time evolution of such states is briefly discussed.
 Publication:

Ph.D. Thesis
 Pub Date:
 1992
 Bibcode:
 1992PhDT........15R
 Keywords:

 Classical Mechanics;
 Hamiltonian Functions;
 Jacobi Matrix Method;
 Kepler Laws;
 Oscillators;
 Quantum Mechanics;
 Coordinates;
 Equations Of Motion;
 Time Functions;
 Thermodynamics and Statistical Physics