HAMILTON-JACOBI DYNAMICS FOR THE SOLUTION OF TIME-DEPENDENT QUANTUM PROBLEMS .1. FORMALISM AND WAVE-PACKET PROPAGATION IN ONE-DIMENSION

Two methods for the numerical integration of the time-dependent Schrod inger equation with given initial conditions (initial wave packet) are presented. The first method (method A) is based on the Schrodinger re presentation of the quantum-dynamical system while the second one (met hod B) is based upon the intermediate representation. In both cases th e quantum dynamical equation is transformed into a system of Hamilton- Jacobi type equations of motion as occurring in multi particle classic al dynamics, i.e. standard molecular dynamics techniques can be applie d for the integration. The dynamics of a minimum uncertainty Gaussian wave packet in a strongly anharmonic oscillator is taken as an example .