Geodesic
Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets)
Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 1, pp. 64-86

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Constructing the basic operators of scattering theory on and off the mass shell in terms of spatially bounded stationary wave packets or proper differentials is described. For this, we use a technique based on a certain scheme for discretizing the continuum. Finite-dimensional approximations for the Green's functions and $T$-matrix, which are first found here, are immediately constructed for any energy using a single simple diagonalization of the Hamiltonian matrix in an $L_2$-type complete basis. We show that the developed approach leads to a convenient finite-dimensional representation of the scattering operators in the basis of the wave functions of a harmonic oscillator. The method allows an immediate extension to the problem of three and more bodies. 
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     author = {V. I. Kukulin and O. A. Rubtsova},
     title = {Formulation of {Quantum} {Scattering} {Theory} in {Terms} of {Proper} {Differentials} {(Stationary} {Wave} {Packets)}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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V. I. Kukulin; O. A. Rubtsova. Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets). Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 1, pp. 64-86. http://geodesic.mathdoc.fr/item/TMF_2002_130_1_a4/