Quantum Scattering Sample Clauses

Quantum Scattering. ‌ In this section we give a summary of the framework for quantum resonant scattering, closely following the presentation in [14]. The model of quantum scattering has as a starting point the decomposition of the system into an asymptotic and an interacting region. The interacting region is compact and the associated Xxxxxxx space is spanned by orthonormal states |n⟩. The asymptotic region is associated with a continuum of states |E, m⟩, labelled by the energy E and a channel index m ranging from 1 to M . The channel index summarises quantum numbers such as the spin and angular momentum in nuclear scattering or the transverse mode of a semi-infinite waveguide attached to a cavity. An example of such a cavity is shown in fig. 1, where the states |n⟩ correspond to solutions of the Schr¨odinger equation in the cavity without the leads and the states |E, m⟩ are solutions of the free Schr¨odinger equation in the leads. In this case m will label the transverse modes of the leads.
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