``Fall toward the centre'' in quasipotential theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 59 (1984) no. 1, pp. 58-69
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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 $n=1$).
@article{TMF_1984_59_1_a3,
author = {V. Sh. Gogokhiya},
title = {``Fall toward the centre'' in quasipotential theory},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {58--69},
publisher = {mathdoc},
volume = {59},
number = {1},
year = {1984},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1984_59_1_a3/}
}
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/