In this paper the quantum direct scattering problem is solved for the Sine-Gordon model. Correlators of the Jost functions are derived by the angular quantization method. November, 93 † On leave of absence from L.D. Landau Institute for Theoretical Physics, Kosygina 2, Moscow, Russia ∗ e-mail address: [email protected]

The purpose of this study is to examine the properties scattering solutions and function an impulsive Sturm-Liouville boundary value problem on semi axis. By using Jost solutions, we obtain function, asymptotic representation resolvent operator. Finally, unperturbated equation.

We consider the class of CMV operators with super-exponentially decaying Verblunsky coefficients. For these we define the concept of a resonance. Then we prove the existence of Jost solutions and a uniqueness theorem for the inverse resonance problem: Given the location of all resonances, taking multiplicities into account, the Verblunsky coefficients are uniquely determined.

We calculate Bardeen-Cooper-Schrieffer (BCS) state of a unitary Fermi gas atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for resonant interactions [2019 {\rm J. Phys. B: At. Mol. Opt. Phys.} {\bf 52}, 165004]. Using exact scattering solution potential, we derive two-body ${\mathbf T}$-matrix element is employed construct BCS Hamiltonian in ...

It is well known that the s-wave Jost function for a potential, λV , is an entire function of λ with an infinite number of zeros extending to infinity. For a repulsive V, and at zero energy, these zeros of the ”coupling constant”, λ, will all be real and negative, λn(0) < 0. By rescaling λ, such that λn < −1/4, and changing variables to s, with λ = s(s − 1), it follows that as a function of s t...