Moshinsky function

Quantum transients are temporary features that appear in the time evolution of matter waves before they reach a stationary regime. They usually arise as a result of a sudden switch interaction that modifies the confinement of particles in a spatial region or after the preparation of a decaying sfafe [48]. The archetypical quantum transient phenomena is diffraction in time which consists of the sudden opening of a shutter to release a semi-infinite beam producing temporal and spatial oscillations of the time evolving wave [49]. A common feature in the mathematical description of quantum transient phenomena is the Moshinsky function, which as we have seen is closely related to the Faddeyeva function. Since in a recent review [48] there appears a discussion on transient phenomena for the dynamics of tunneling based on the present resonant state formalism [54, 66-76], here we restrict the discussion to the time evolution of quantum decay. 

The properfies of fhe Moshinsky function may be obtained from fhe prop-erfies of fhe function exp (y ) erfc(y ). It turns out that this last product corresponds to the Faddeyeva function w(v) = exp (- o )erfc( - iv) as defined by Abramowifz and Sfegun [51] and Faddeyeva and Terentev [50]. Hence making v = iy one may write the Moshinsky function as... 

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