Comment on the article by Bender et al, J. Phys. A 35, L467 (2002)

TL;DR

This paper critically discusses Bender et al.'s claims about PT-invariant Hamiltonians, highlighting limitations due to their approximations and questioning the broader implications of their symmetry-based approach.

Contribution

It provides a critical commentary on the symmetry arguments used by Bender et al., emphasizing the approximations that weaken their conclusions.

Findings

Identifies limitations in Bender et al.'s symmetry arguments

Highlights the impact of approximations on the results

Questions the generality of the 'demystification' claim

Abstract

The recent Letter by Bender, Berry, and Mandilara (2002, BBM) presents some interesting symmetry arguments which enable one to transform non-hermitian, PT invariant, (complex) polynomial potential hamiltonians, into secular equation representations with real coefficients. This achievement is claimed to ``demistify'' why these systems can admit real and/or complex eigenenergies. Two approximations underly their arguments, and weaken the implied significance of their work.