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arXiv · 1002.1221

Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions

Hossein Mehri-Dehnavi·Ali Mostafazadeh·Ahmet Batal
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Abstract

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+ζ_-δ(x+a)+ζ_+δ(x-a), where ζ_\pm and a are respectively complex and real parameters and δ(x) is the Dirac delta function. For regions in the space of coupling constants ζ_\pm where H is quasi-Hermitian and there are no complex bound states or spectral singularities, we construct a (positive-definite) metric operator ηand the corresponding equivalent Hermitian Hamiltonian h. ηturns out to be a (perturbatively) bounded operator for the cases that the imaginary part of the coupling constants have opposite sign, \Im(ζ_+) = -\Im(ζ_-). This in particular contains the PT-symmetric case: ζ_+ = ζ_-^*. 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.

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Hossein Mehri-Dehnavi, Ali Mostafazadeh, Ahmet Batal. 2010-06-02. Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions. https://doi.org/10.1088/1751-8113%2F43%2F14%2F145301

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