Schrödinger operator with a junction of two 1-dimensional periodic potentials

Evgeny Korotyaev

The spectral properties of the Schrödinger operator $T_{t}y=-y^{\prime \prime }+q_{t}y$ in $L^2(\mathbb{R})$ are studied, with a potential $q_t(x)=p_1(x),x<0,$ and $q_t(x)=p(x+t),x>0,$ where $p_1,p$ ar…