Physics – Quantum Physics
Scientific paper
2010-02-05
J. Phys. A 43, 145301 (2010)
Physics
Quantum Physics
22 pages, 4 figures
Scientific paper
We present a generalization of the perturbative construction of the metric operator for non-Hermitian Hamiltonians with more than one perturbation parameter. We use this method to study the non-Hermitian scattering Hamiltonian: H=p^2/2m+\zeta_-\delta(x+a)+\zeta_+\delta(x-a), where \zeta_\pm and a are respectively complex and real parameters and \delta(x) is the Dirac delta function. For regions in the space of coupling constants \zeta_\pm where H is quasi-Hermitian and there are no complex bound states or spectral singularities, we construct a (positive-definite) metric operator \eta and the corresponding equivalent Hermitian Hamiltonian h. \eta turns out to be a (perturbatively) bounded operator for the cases that the imaginary part of the coupling constants have opposite sign, \Im(\zeta_+) = -\Im(\zeta_-). This in particular contains the PT-symmetric case: \zeta_+ = \zeta_-^*. We also calculate the energy expectation values for certain Gaussian wave packets to study the nonlocal nature of $\rh$ or equivalently the non-Hermitian nature of $\rH$. We show that these physical quantities are not directly sensitive to the presence of PT-symmetry.
Batal Ahmet
Mehri-Dehnavi Hossein
Mostafazadeh Ali
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