Geodesic
“Fall toward the centre” in quasipotential theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 59 (1984) no. 1, pp. 58-69 
V. Sh. Gogokhiya. “Fall toward the centre” in quasipotential theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 59 (1984) no. 1, pp. 58-69. http://geodesic.mathdoc.fr/item/TMF_1984_59_1_a3/
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     author = {V. Sh. Gogokhiya},
     title = {{\textquotedblleft}Fall toward the centre{\textquotedblright} in quasipotential theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A study is made of the quasipotential equation for the wave function in the momentum space in the case of the singular attractive potential $U(r)=-\lambda r^{-2}$. It is shown that in the nonrelativistic limit the discrete spectrum does not depend on the arbitrary constant and is characterized by the presence of a finite ground state, i.e., in it there is no “fall toward the center” problem. These results are a consequence of the self-adjointness of the quasipotential operator in the momentum space (deficiency index $n=0$), in contrast to the Lippmann-Schwinger operator (deficiency index $n=1$).

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