LXXIV International conference Nucleus-2024: Fundamental problems and applications

Diffractionless solutions for the bound states of the model 1D three-body problem

2 Jul 2024, 11:15

15m

Second floor Hall (BLTP)

Oral Nuclear structure: theory and experiment

Speaker

Anastasiya Malykh (BLTP JINR)

Description

The model of the one-dimensional impenetrable particles with interactions via the boundary conditions is considered. This model, besides its relation to the three-body problem [1-3],
describes also the wave diffraction problem for
the impedance wedge [4]. Previously, an exact solution was obtained by means of the Maluzhinetz-Sommerfeld transformation [4,2,3]. In the present report it was found that the bound-state solution turns out to be in the diffractionless (Bethe ansatz) form. A simple analytical expression for the eigenvalues is given. The relation to this model problem to the zero-range interaction problem [5] is discussed.

References

[1] E. Lieb and H. Koppe, Phys. Rev. 116, 367 (1959).
[2] J.B. McGuire and C.A. Hurst, J. Math. Phys. 13,
1595-1607 (1972).
[3] K. Lipszyc, J. Math. Phys. 21, 1092–1102 (1980).
[4] G. D. Maluzhinetz, Dokl. Akad. Nauk SSSR 121, 436-439 (1958).
[5] O.I. Kartavtsev, A.V.Malykh, S.A. Sofianos, ZhETF 135,
419 (2009).