Comment on: ?Numerical estimates of the spectrum for anharmonic PT symmetric potentials?

P. AMORE; F. M. FERNÁNDEZ

PHYSICA SCRIPTA - (Print)

IOP PUBLISHING LTD

Lugar: Londres; Año: 2013 vol. 87 p. 47001 - 47001

0031-8949

We show that the authors of the commented paper (Bowen et al 2012 Phys. Scr. 85 065005)draw their conclusions from the eigenvalues of truncated Hamiltonian matrices that do notconverge as the matrix dimension increases. In some of the studied examples, the authorsmissed the real positive eigenvalues that already converge towards the exact eigenvalues of thenon-Hermitian operators and focused their attention on the complex ones that do not. We alsoshow that the authors misread Bender?s argument about the eigenvalues of the harmonicoscillator with boundary conditions in the complex-x plane (Bender 2007 Rep. Prog. Phys.70 947)