Geodesic
The levels of the two-particle Schr\"odinger operator corresponding to
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 229-239

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For a two-particle Schrödinger operator considered in a cell and having a potential periodic in four variables, we establish the existence of levels {(}i.e., eigenvalues or resonances{\rm)} in the neighborhood of singular points of the unperturbed Green's function and derive an asymptotic formula for these levels. We prove an existence and uniqueness theorem for the solution of the corresponding Lippmann–Schwinger equation.
Keywords: two-particle Schrödinger operator, Lippmann–Schwinger equation, resonance, eigenvalue. 
@article{TMF_2006_147_2_a1,
     author = {Yu. P. Chuburin},
     title = {The levels of the two-particle {Schr\"odinger} operator corresponding to},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {229--239},
     publisher = {mathdoc},
     volume = {147},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a1/}
}
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Yu. P. Chuburin. The levels of the two-particle Schr\"odinger operator corresponding to. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 229-239. http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a1/