A Matzkin 2006 J. Phys. A: Math. Gen. 39 10859 doi:10.1088/0305-4470/39/34/017
Non-Hermitian quantum mechanics: the case of bound state scattering theory
A Matzkin
Show affiliationsExcited bound states are often understood within scattering-based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert spaces and metric operator relevant to a correct formulation of such theories. The structure and tools employed are the same that have been introduced in current works dealing with PT-symmetric and quasi-Hermitian problems. The relevance of the non-Hermitian formulation to practical computations is assessed by introducing a non-Hermiticity index. We give a numerical example involving scattering by a short-range potential in a Coulomb field for which it is seen that even for a small but non-negligible non-Hermiticity index the non-Hermitian character of the problem must be taken into account. The computation of physical quantities in the relevant Hilbert spaces is also discussed.
- PACS
- MSC
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81Uxx Scattering theory (See also 34A55, 34L25, 34L40, 35P25, 47A40)
- Subjects
- Dates
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Issue 34 (25 August 2006)
Received 4 April 2006, in final form 3 July 2006
Published 9 August 2006
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Non-Hermitian quantum mechanics: the case of bound state scattering theory
A Matzkin 2006 J. Phys. A: Math. Gen. 39 10859
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