Abstract
This paper investigates finite-dimensional PT-symmetric Hamiltonians. It is shown here that there are two ways to extend real symmetric Hamiltonians into the complex domain: (i) The usual approach is to generalize such Hamiltonians to include complex Hermitian Hamiltonians. (ii) Alternatively, one can generalize real symmetric Hamiltonians to include complex PT-symmetric Hamiltonians. In the first approach the spectrum remains real, while in the second approach the spectrum remains real if the PT symmetry is not broken. Both generalizations give a consistent theory of quantum mechanics, but if D>2, a D-dimensional Hermitian matrix Hamiltonian has more arbitrary parameters than a D-dimensional PT-symmetric matrix Hamiltonian.
Similar content being viewed by others
References
C.M. Bender, P.N. Meisinger, and Q. Wang: J. Phys. A 36 (2003) 6791.
W.-K. Tung: Group Theory in Physics, World Scientific, Philadelphia, 1985.
C.M. Bender, D.C. Brody, and H.F. Jones: Phys. Rev. Lett. 89 (2002) 270402.
A. Mostafazadeh: J. Phys. A 36 (2003) 7081.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wang, Q. Finite-Dimensional PT-Symmetric Hamiltonians. Czechoslovak Journal of Physics 54, 143–146 (2004). https://doi.org/10.1023/B:CJOP.0000014379.56634.4f
Issue Date:
DOI: https://doi.org/10.1023/B:CJOP.0000014379.56634.4f