The fact that eigenvalues of PT-symmetric Hamiltonians H can be real for some values of a parameter and complex for others is explained by showing that the matrix elements of H, and hence the secular equation, are real, not only for PT but also for any antiunitary operator A satisfying A2k = 1 with k odd. The argument is illustrated by a 2 × 2 matrix Hamiltonian, and two examples of the generalization are given.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)