Two-Body Scattering with Wave Packets

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Abstract
Two‐body scattering is analyzed using a time‐dependent formalism and wave packets of arbitrary shape as the initial wavefunctions. In particular, the case of single‐channel resonant scattering is discussed in some detail. In addition to the usual amplitudes resulting from the potential term and the resonant term, a third amplitude is found which interferes with the other two. Another interesting result is that in this formalism the final state is not necessarily represented by spherical outgoing waves, but can be interpreted instead as two separate outgoing wave packets whose shape is different from the initial packets. The Wigner time delay is obtained as a natural consequence of the analysis, and the resonant cross sections are expressed as density matrices constructed from the wave packets.

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