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On the Bound State of three Particles
Author(s) -
Zakhariev B. N.,
Kalinauskas R. K.
Publication year - 1965
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19654710702
Subject(s) - physics , bound state , state (computer science) , function (biology) , energy (signal processing) , mathematical physics , motion (physics) , population , particle (ecology) , combinatorics , classical mechanics , quantum mechanics , mathematics , oceanography , demography , algorithm , evolutionary biology , sociology , biology , geology
The expansion of the function Ψ of three particles interacting with each other via the potentials V 12 ; V 13 ; V 23 in a complete set of the functions describing the motion of two particles coupled by a finite potential well V 12 (the complex particle) is considered. It is shown that in this expansion the population of the highest virtual states decreases with energy as \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{\varepsilon }{{\mathop \varepsilon \nolimits_n^3 }} $\end{document} . The system of integral differential equations for the bound state of three particles can be cut off (all the ϕ n in (9) with ϵ n > ϵ s , where ϵ s is rather large, may be neglected).