Quasi-exactly-solvable confining solutions for spin-1 and spin-0 bosons in (1+1)-dimensions with a scalar linear potential

TL;DR

This paper corrects previous misconceptions and provides exact bound-state solutions for spin-0 and spin-1 bosons in (1+1) dimensions with a scalar linear potential, using generalized Laguerre polynomials.

Contribution

It offers a proper derivation of confining solutions in the Duffin-Kemmer-Petiau framework, clarifying the dependence on potential parameters and quantum numbers.

Findings

Proper bound-state solutions expressed via generalized Laguerre polynomials

Eigenvalues depend on algebraic equations involving potential and quantum number

Corrects previous misleading treatments in the literature

Abstract

We point out a misleading treatment in the recent literature regarding confining solutions for a scalar potential in the context of the Duffin-Kemmer-Petiau theory. We further present the proper bound-state solutions in terms of the generalized Laguerre polynomials and show that the eigenvalues and eigenfunctions depend on the solutions of algebraic equations involving the potential parameter and the quantum number.