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Quantum Scattering Theory

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An Introduction to Cold and Ultracold Chemistry

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Abstract

This chapter revolves around the theoretical minimum scattering theory to understand the main physical and chemical processes at cold and ultracold temperatures. The concept of scattering is introduced based on experimental grounds, followed by the classical and quantum definitions of the cross section. In this way, we hope to emphasize the main difference between the quantum and classical realms. Within the quantum theory of scattering, we pay special attention to the concept of scattering length and Wigner threshold laws owing to its importance in ultracold chemistry. In addition, we introduce some quantum mechanical effects on scattering observables such as Fano–Feshbach resonances and the glory effect, which is a very well-known phenomenon in chemical physics.

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Notes

  1. 1.

    This is Green’s function for the two-body Schrödinger equation in spherical coordinates [2, 3].

  2. 2.

    This is only true for bosons. For fermions the lowest partial wave is l = 1.

  3. 3.

    A partial wave is each of the centrifugal quantum numbers, l, that contribute to the scattering process at a given collision energy.

  4. 4.

    We should talk about quasi-bound states, since they are above the threshold of the entrance and channel, and hence they are not truly bound states.

  5. 5.

    The refraction index in optics is analogous to the role of potential on classical mechanics [46, 47].

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Authors and Affiliations

  1. Fritz Haber Institute of the Max Planck Society, Department of Molecular Physics, Berlin, Germany

    Jesús Pérez Ríos

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  1. Jesús Pérez Ríos
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Pérez Ríos, J. (2020). Quantum Scattering Theory. In: An Introduction to Cold and Ultracold Chemistry. Springer, Cham. https://doi.org/10.1007/978-3-030-55936-6_2

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