On stable $\mathcal{C}$-symmetries for a class of $\mathcal{PT}$-symmetric operators

Abstract

Recently, much attention is paid to the consideration of physical models described by $\mathcal{PT}$-symmetric Hamiltonians. In this paper, we establish a necessary and sufficient condition for existence of a stable $\mathcal{C}$-symmetry for a class of $\mathcal{PT}$-symmetric extensions of a symmetric operator $S$ with deficiency indices $(2,2)$.