Geodesic
On the trace-class method in potential scattering theory
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 20, Tome 171 (1989), pp. 12-35

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One considers a perturbation of Schrödinger operator $H_0$ with an arbitrary bounded potential by a function $q$ which is vanishing sufficiently quickly at infinity. Trace-class theorems are applied to prove existence and completeness of wave operators for corresponding Hamiltonians $H_0$, $H=H_0+q$. Generalizations to broader class of unperturbed operators as well as to perturbations by first-order differential operators are given. Moreover, perturbations by integral operators of Fourier type are considered. 
@article{ZNSL_1989_171_a1,
     author = {M. Sh. Birman and D. R. Yafaev},
     title = {On the trace-class method in potential scattering theory},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {12--35},
     publisher = {mathdoc},
     volume = {171},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_171_a1/}
}
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M. Sh. Birman; D. R. Yafaev. On the trace-class method in potential scattering theory. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 20, Tome 171 (1989), pp. 12-35. http://geodesic.mathdoc.fr/item/ZNSL_1989_171_a1/