Non-Hermitian quantum mechanics: the case of bound state scattering theory

Details Non-Hermitian quantum mechanics: the case of bound state scattering theory Non-Hermitian quantum mechanics: the case of bound state scattering theory

2006-03-26

arxiv.org/abs/quant-ph/0603238v1

J. Phys. A: Math. Gen. 39, 10859, 2006

Physics

Quantum Physics

Scientific paper

10.1088/0305-4470/39/34/017

Excited 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.

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