Localized Modes of the Linear Periodic Schrödinger Operator with a Nonlocal Perturbation
Localized Modes of the Linear Periodic Schrödinger Operator with a Nonlocal Perturbation
We consider the existence of localized modes corresponding to eigenvalues of the periodic Schrödinger operator $-\partial_x^2+V(x)$ with an interface. The interface is modeled by a jump either in the value or the derivative of $V(x)$ and, in general, does not correspond to a localized perturbation of the perfectly periodic operator. …