Abstract
In the paper the so-called “Resonance-Decay Problem in Quantum Mechanics” is solved for a selected class of Hamiltonians: The absolutely continuous part of the Hamiltonian is unitarily equivalent to a selfadjoint operator \( H \) on the Hilbert space \( \mathcal{H}_+\,\,:= L^2(\mathbb{R}_+,\,\mathcal{K},\,d\lambda),\,\mathcal{K} \) the multiplicity space, such that \( H \) together with the multiplication operator on \( \mathcal{H}_+ \) forms an asymptotic complete scatterings ystem such that the scattering matrix \( S(.) \) is holomorphic in the upper half-plane and satisfies certain conditions at 0, at infinity and on the rim \( \mathbb{R}\_\,\,+i0 \). The proof uses methods of the Lax-Phillips scatteringtheo ry.
Mathematics Subject Classification (2010). 81Q10, 47A40, 47D06.
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Dedicated to Arno Bohm
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Baumgärtel, H. (2013). The Resonance-Decay Problem in Quantum Mechanics. In: Kielanowski, P., Ali, S., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0448-6_14
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DOI: https://doi.org/10.1007/978-3-0348-0448-6_14
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