A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in $\mathbb{R}$

Zhijie Chen, Erjuan Fu, Chang-Shou Lin

In this paper, we study the spectrum of the complex Hill operator $L=\frac{d^2}{d{x}^2}+q(x;\tau )$ in $L^2(\mathbb{R},\mathbb{C})$ with the Darboux-Treibich-Verdier potential \[q(x;τ):=…