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Asymptotic behavior of the wave function of three particles in a continuum

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Abstract

We study the wave function of a system of three particles in a continuum. The Faddeev equations are used to explicitly identify the singularities of the wave function in the momentum space. We obtain the asymptotic behavior of the wave function in the configuration space by calculating the asymptotic behavior of the Fourier transform of the wave function in the momentum space. Our attention is focused on configurations in which two particles are at a relatively small distance from each other while the third particle is significantly remote from the center of mass of the pair. We show that the coordinate asymptotic form of the wave function for such a configuration contains scattered waves of a new type in addition to the standard terms. We use the obtained exact data concerning the coordinate asymptotic form of the wave function to critically analyze the multiplicative ansatz used in several works to describe systems of three particles in a continuum.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    S. L. Yakovlev

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  1. S. L. Yakovlev
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Correspondence to S. L. Yakovlev.

Additional information

This paper is dedicated to the memory of Academician S. P. Merkuriev on his 70th birthday

This research is supported by St. Petersburg State University (Grant No. 11.38.241.2015), the Russian Foundation for Basic Research (Grant No. 14-02-00326), and the Program for Supporting Leading Scientific Schools (Grant No. NSh-1292.2014.1).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 186, No. 1, pp. 152–163, January, 2016.

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Yakovlev, S.L. Asymptotic behavior of the wave function of three particles in a continuum. Theor Math Phys 186, 126–135 (2016). https://doi.org/10.1134/S0040577916010116

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