HAMILTON-JACOBI DYNAMICS FOR THE SOLUTION OF TIME-DEPENDENT QUANTUM PROBLEMS .2. WAVE-PACKET PROPAGATION IN 2-DIMENSIONAL, NONLINEARLY COUPLED OSCILLATORS - EXACT AND TIME-DEPENDENT SCF-SOLUTIONS

Methods for the approximate numerical integration of the time dependent Schrodinger equation with given initial conditions (the initial wave packet) are presented. The methods are based on the Schrodinger representation of the quantum dynamic system. The quantum dynamic equations are transformed into Hamilton-Jacobi type equations of motion as they occur in multi particle classical dynamics, i.e. standard techniques in molecular dynamics can be applied for the integration. The dynamics of minimum uncertainty Gaussian wave packets in strongly nonharmonic, nonlinearly coupled oscillators are studied as examples. The numerically exact solutions are compared to time dependent SCF approximations of the wave packet.