On eigenstates for some $sl_2$ related Hamiltonian

zbMATH Open1438.81019arXiv1707.01193MaRDI QIDQ5237960

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Publication date: 25 October 2019

Abstract: In this paper we consider the stationary Schroedinger equation for a self-conjugated Hamiltonian $H=frace+fi$, where $e$ and $f$ is an anti-unitary pair of the canonical Cartan "creating" and "annihilation" operators for the classical Lie algebra $s{l}_2$ taken in the representation with "the lowest weight equals to $1$". In this paper we prove that this operator has the continuous spectrum. Construction of eigenstates for $H$ is given in details.

Full work available at URL: https://arxiv.org/abs/1707.01193

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