Entire functions, PT-symmetry and Voros's quantization scheme

TL;DR

This paper links Avila's theorem on Voros's quantization to PT-symmetric eigenvalue reality, proving a special case of a conjecture by Bender, Boettcher, and Meisinger.

Contribution

It establishes a connection between exact quantization convergence and PT-symmetry eigenvalue reality, proving a key conjecture case.

Findings

Proved a special case of the eigenvalue reality conjecture.

Linked Voros's quantization scheme to PT-symmetric boundary problems.

Validated the convergence of Voros's quantization in this context.

Abstract

In this paper, A. Avila's theorem on convergence of the exact quantization scheme of A. Voros is related to the reality proofs of eigenvalues of certain PT-symmetric boundary value problems. As a result, a special case of a conjecture of C. Bender, S. Boettcher and P. Meisinger on reality of eigenvalues is proved.