Quantum Time-Dependent and Time-Independent Three- Body Rearrangement Collisions in Hyperspherical Coordinates
We present both time-‐independent and time-‐dependent methods for accurately and efficiently solving the quantum Schrodinger equation using hyperspherical coordinates. A new time-‐dependent wave packet method is presented and compared to our time-‐independent method for extracting state-‐to-‐state S-‐matrix elements. This new method expresses the wave packet in a democratic set of (APH) coordinates during the evolution in time. Product channel eigenfunctions are projected onto the propagated wave packet along a fixed asymptotic hyperradius at each time step. The S matrix elements are proportional to the Fourier transform of the projection coefficients.
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