Geodesic
“Fall toward the centre” in quasipotential theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 59 (1984) no. 1, pp. 58-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $n=1$). 
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     title = {{\textquotedblleft}Fall toward the centre{\textquotedblright} in quasipotential theory},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1984_59_1_a3/}
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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/

[1] Case K. M., Phys. Rev., 80:5 (1950), 797–806 | DOI | MR | Zbl

[2] De Alfaro V., Redzhe T., Potentsialnoe rasseyanie, Mir, M., 1966 | Zbl

[3] Nyuton R., Teoriya rasseyaniya voln i chastits, Mir, M., 1969 | MR

[4] Perelomov A. M., Popov V. S., TMF, 4:1 (1970), 48–65 | MR

[5] Filippov A. T., EChAYa, 10:3 (1979), 501–538 | MR

[6] Meetz K., Nuovo Cim., 34:3 (1964), 690–708 | DOI | MR | Zbl

[7] Behncke E., Nuovo Cim., 55A:4 (1968), 780–785 | DOI

[8] Logunov A. A., Tavkhelidze A. N., Nuovo Cim., 29:2 (1963), 380–399 | DOI | MR

[9] Tavkhelidze A. N., “Kvazipotentsialnyi metod v kvantovoi teorii polya”, Trudy mezhdunarodnoi zimnei shkoly po teoreticheskoi fizike, t. 2, OIYaI, Dubna, 1964, 66–79

[10] Kadyshevskii V. G., Tavkhelidze A. N., “Kvazipotentsialnyi metod v relyativistskoi zadache dvukh tel”, Problemy teoreticheskoi fiziki, Sbornik, posvyaschennyi N. N. Bogolyubovu v svyazi s ego shestidesyatiletiem, Nauka, M., 1969, 261–277 | MR

[11] Faustov R. N., EChAYa, 3:1 (1975), 238–268

[12] Frank N. M., Land D. J., Spector R. M., Rev. Mod. Phys., 43:1 (1971), 36–98 | DOI | MR

[13] Gogokhiya V. Sh., Filippov A. T., TMF, 21:1 (1974), 37–48 | MR | Zbl

[14] Gogokhiya V. Sh., Mavlo D. P., Filippov A. G., TMF, 27:3 (1976), 323–336

[15] Landau L. D., Lifshits E. M., Kvantovaya mekhanika, Fizmatgiz, M., 1963

[16] Gogokhiya V. Sh., TMF, 48:1 (1981), 80–88 | MR

[17] Gogokhiya V. Sh., Reshenie kvazipotentsialnykh zadach Shturma - Liuvillya metodom etalonnogo uravneniya, Preprint R2–82–186, OIYaI, Dubna, 1982

[18] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, Nauka, M., 1965 | MR

[19] Devis F., “Gamma-funktsiya i rodstvennye ei funktsii”, Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979, 80–118

[20] Filippov A. T., “Teoriya potentsialnogo rasseyaniya i nekotorye ee obobscheniya”, Trudy mezhdunarodnoi zimnei shkoly po teoreticheskoi fizike, t. 2, OIYaI, Dubna, 1964, 80–107

[21] Gogokhiya V. Sh., Soobscheniya AN GrSSR, 90:2 (1978), 333–336

[22] Shredinger E., “O svobodnom dvizhenii v relyativistskoi kvantovoi mekhanike”, Izbrannye trudy po kvantovoi mekhanike, Nauka, M., 1976, 218–228 | MR