The use of non-Hermitian Hamiltonians in quantum mechanics [cf.,
e.g., its recent brief review in C. M. Bender, D. C. Brody and H. F.
Jones ``Complex extension of quantum mechanics", Phys. Rev. Letters
89 (2002) 270401] is neither surprizing [for a long time, people are
using less usual scalar products in Hilbert space, e.g., in nuclear
physics: cf. F. G. Scholtz, H. B. Geyer and F. J. W. Hahne,
``Quasi-Hermitian operators in quantum mechanics and the variational
principle", Annals of Physics (NY) 213 (1992) 74-101] nor new
(students encounter their first pseudo-Hermitian Hamiltonian when
studying the Klein-Gordon equation in Feshbach-Villars metric).
Still, once it has been made popular in the pioneering letter by C.
Bender and S. Boettcher in 1998 [cf. ``Real spectra in non-Hermitian
Hamiltonians having PT symmetry", Phys. Rev. Letters 80 (1998) 4243
-- 4246], the problem is studied with renewed intensity. The erratum
in question illustrates very well one of its subtleties (namely, a
trap represented by our habit of using the Hermiticity-related
intuition). In his reaction to the (valid) criticism in ref. [1], A.
Mostafazadeh presents (and proves) the corrected version of the
Theorem which shows how the pseudo-Hermitian H may be understood as
Hermitian after one modifies the scalar product.



CNO: 1953105 Mostafazadeh, Ali . Erratum: "Pseudo-Hermiticity for a
class of nondiagonalizable Hamiltonians" [J. Math. Phys. 43 (2002),
no. 12, 6343--6352; 1940450]. J. Math. Phys. 44 (2003), no. 2, 943.