Finite-Dimensional PT-Symmetric Hamiltonians

Author： Wang Qinghai  

Publisher： Springer Publishing Company

ISSN： 0011-4626

Source： Czechoslovak Journal of Physics, Vol.54, Iss.1, 2004-01, pp. : 143-146

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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.

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