Kh. Yeon et al., PROPAGATOR OF A TIME-DEPENDENT UNBOUND QUADRATIC HAMILTONIAN SYSTEM, Nuovo cimento della Societa italiana di fisica. B, Relativity, classical and statistical physics, 111(8), 1996, pp. 963-971
The propagator for a time-dependent unbound quadratic Hamiltonian syst
em is explicitly evaluated using the path integral method. Two time-in
variant quantities of the system are found where these invariants dete
rmine whether or not the system is bound. Several examples are conside
red to illustrate that the propagator obtained for the unbound systems
is correct.