A complex periodic QES potential and exceptional points

Abstract

We show that the complex $\mathcal{P}\mathcal{T}$-symmetric periodic potential $V(x)=-(\mathrm{i}\xi \sin 2x+N{)}^2$, where $\xi$ is real and $N$ is a positive integer, is quasi-exactly solvable. For odd values of $N\ge 3$, it may lead to exceptional points depending upon the strength of the coupling parameter $\xi$. The corresponding Schrödinger equation is also shown to go over to the Mathieu equation asymptotically. The limiting value of the exceptional points derived in our scheme is consistent with known branch-point singularities of the Mathieu equation.

9 pages, no figure, published version

References in corpus (2)

• Making Sense of Non-Hermitian Hamiltonians
• A return to observability near exceptional points in a schematic PT-symmetric model

Cited by in corpus (2)

• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Non-Hermitian Hamiltonians of Lie algebraic type