Transmission coefficient and two-fold degenerate discrete spectrum of spin-1 bosons in a double-step potential

TL;DR

This paper analyzes how spin-1 bosons scatter in a double-step potential, revealing polarization-insensitive transmission and a two-fold degenerate spectrum through effective Schrödinger equations.

Contribution

It introduces a detailed analysis of spin-1 boson scattering in a double-step potential, highlighting polarization insensitivity and spectral degeneracy.

Findings

Transmission coefficient is polarization-independent.

Existence of a two-fold degenerate spectrum.

Poles of the transmission amplitude indicate bound states.

Abstract

The scattering of spin-1 bosons in a nonminimal vector double-step potential is described in terms of eigenstates of the helicity operator and it is shown that the transmission coefficient is insensitive to the choice of the polarization of the incident beam. Poles of the transmission amplitude reveal the existence of a two-fold degenerate spectrum. The results are interpreted in terms of solutions of two coupled effective Schr\"{o}dinger equations for a finite square well with additional $\delta $-functions situated at the borders.