Small-$ε$ behavior of the Non-Hermitian PT-Symmetric Hamiltonian $H=p^2+x^2(ix)^ε$
The energy eigenvalues of the class of non-Hermitian PT-symmetric Hamiltonians $H=p^2+x^2(ix)^ε$ ($ε\geq0$) are real, positive, and discrete. The behavior of these eigenvalues has been studied perturbatively for small $ε$. However, until now no other features of $H$ have been examined perturbatively. In this paper the small-$ε$ expansion of the C operator and the equivalent isospectral Dirac-Hermitian Hamiltonian $h$ are derived.
hep-th↗