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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2024 Volume 533, Pages 15–43 (Mi znsl7464)

Model of an effective separable potential in the problem of three one-dimensional quantum particles

A. S. Bagmutovab, S. B. Levinca, V. O. Toropovac

a Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg
b St. Petersburg Institute of Precision Mechanics and Optics
c Saint Petersburg State University

Abstract: Bagmutov A. S., Levin S. B., Toropov B. O. Model of an effective separable potential in the problem of three one-dimensional quantum particles. In this paper, we construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range) attractive pair potentials that support bound states. The asymptotic nature of the solution is determined by the rapid decrease of its residual in the Schr?dinger equation.

Key words and phrases: quantum three-body problem, one-dimensional particles, finite pair, attractive potentials, effective separable potentials.

UDC: 517

Received: 02.09.2024



© Steklov Math. Inst. of RAS, 2025