Abstract
For a system of three charged particles the Faddeev equations are derived in the total-angular-momentum representation. They have the form of coupled sets of partial differential equations in three-dimensional space and can be used to develop new efficient numerical procedures to tackle the three-body Coulomb problem. The asymptotic conditions at large distances corresponding both to binary scattering and bound-state problems are presented. The behaviour of the Faddeev components near the triple and double collision points is studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Merkuriev, S. P., Faddeev, L. D.: Quantum Scattering Theory for Few-Body Systems. Moscow: Nauka 1985 (in Russian); Merkuriev, S. P.: Ann. Phys. (NY)130, 395 (1980)
Lim, T. K., Bao, C. G., Hou, D. P., Huber, H. S. (eds.): Few-Body Methods: Principles and Applications. Singapore: World Scientific 1985
Kvitsinsky, A. A., Kuperin, Yu. A., Merkuriev, S. P., Motovilov, A. K., Yakovlev, S. L.: Elem. Part. and Atom. Nucl.17, 267 (1986) (in Russian)
Kostrykin, V. V., Kvitsinsky, A. A., Merkuriev, S. P.: LOMI Preprint E-10-87, Leningrad 1987; Abstracts of Int. Conf. on the Theory of Few-Body and Quark-Hadronic Systems. Dubna 1987, p. 42
Curtis, C. F., Hirschfelder, J. O., Adler, F.: J. Chem. Phys.18, 1638 (1950)
Vinitsky, S. I., Ponomarev, L. I.: Part. Nucl.13, 557 (1982); Vinitsky, S. I., Kaschiev, M. S.: Yad. Fiz.44, 386 (1986) (in Russian)
Omnes, R. L.: Phys. Rev.134B, 1358 (1964)
Fock, V. A.: Izv. Akad. Nauk SSSR, Ser. Fiz.18, 161 (1954) (in Russian); D. Kgl. Norske Videnskab. Selsk. Forth.31, 138 (1958)
Demkov, Yu. N., Ermolaev, A. M.: Sov. Phys. JETP36, 633 (1959)
Vinitsky, S. I., Melezhik, V. S., Ponomarev, L. I.: Sov. J. Nucl. Phys.36, 272 (1982)
Fano, U.: Rep. Progr. Phys.46, 97 (1983)
Morgan, J. D.: Theor. Chim. Acta69, 181 (1986)
Abramowitz, M., Stegun, I. A.: Handbook of Mathematical Functions. Washington, DC: National Bureau of Standards 1964
Merkuriev, S. P., Almazov, A. A.: Lett. Math. Phys.8, 47 (1984)
Messiah, A.: Quantum Mechanics. Amsterdam: North-Holland 1961
Biedenharn, L. C., Louck, J. D.: Angular Momentum in Quantum Physics. Reading, MA: Addison-Wesley 1981
Morse, P. M., Feshbach, H.: Methods of Theoretical Physics. New York: McGraw-Hill 1953
Sundman, K.: Acta Soc. Sci. Fenn.35 (1969)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kostrykin, V.V., Kvitsinsky, A.A. & Merkuriev, S.P. Faddeev approach to the three-body problem in total-angular-momentum representation. Few-Body Systems 6, 97–113 (1989). https://doi.org/10.1007/BF01080553
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01080553