Bender-Wu singularities

Abstract

We consider a family of quantum Hamiltonians $H_{\hslash }=-{\hslash }^2(d^2/d{x}^2)+V(x)$, $x\in \mathbb{R},$ $\hslash >0,$ where $V(x)=i(x^3-x)$ is an imaginary double well potential. We prove the existence of infinite eigenvalue crossings with the selection rules of the eigenvalue pairs taking part in a crossing. This is a semiclassical localization effect. The eigenvalues at the crossings accumulate at a critical energy for some of the Stokes lines.

Cited by in corpus (1)

• Relativistic levels of mesic atoms