Application of pseudo-Hermitian quantum mechanics to a PT-symmetric Hamiltonian with a continuum of scattering states
- Department of Mathematics, Koc University, 34450 Sariyer, Istanbul (Turkey)
We extend the application of the techniques developed within the framework of the pseudo-Hermitian quantum mechanics to study a unitary quantum system described by an imaginary PT-symmetric potential v(x) having a continuous real spectrum. For this potential that has recently been used, in the context of optical potentials, for modeling the propagation of electromagnetic waves traveling in a waveguide half and half filled with gain and absorbing media, we give a perturbative construction of the physical Hilbert space, observables, localized states, and the equivalent Hermitian Hamiltonian. Ignoring terms of order three or higher in the non-Hermiticity parameter {zeta}, we show that the equivalent Hermitian Hamiltonian has the form p{sup 2}/2m+({zeta}{sup 2}/2){sigma}{sub n=0}{sup {infinity}}{l_brace}{alpha}{sub n}(x),p{sup 2n}{r_brace} with {alpha}{sub n}(x) vanishing outside an interval that is three times larger than the support of v(x), i.e., in 2/3 of the physical interaction region the potential v(x) vanishes identically. We provide a physical interpretation for this unusual behavior and comment on the classical limit of the system.
- OSTI ID:
- 20699501
- Journal Information:
- Journal of Mathematical Physics, Vol. 46, Issue 10; Other Information: DOI: 10.1063/1.2063168; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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