Abstract
Most of what we know about the structure of matter comes from scattering experiments. When I discuss scattering in 3-D, I will review classical scattering theory, but for the time being, I want to discuss the scattering problem in one dimension. Scattering is simple in principle - send something in and see what comes out. I will give a detailed analysis of scattering in one dimension for the step potential shown in Fig. 17.1 and then give a qualitative discussion for other potentials. The step potential can be written as V (x) = V (x) = V 0 Θ(x), where Θ(x) is the Heaviside step function which is zero for x < 0 and one for x ≥ 0.
Step potential: (a) Energy less than the barrier height. (b) Energy greater than the barrier height
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Notes
- 1.
The dependence of the time delay on β is similar to that encountered in the dependence of the scattering length (the scattering length is discussed in Chap. 18) on magnetic field strength when the field is used to tune the energy in an open scattering channel to that of a bound state in a closed channel of the intermolecular potentials. Such Feshbach resonances play an important role in controlling interactions in Bose-Einstein condensates [for a review, see the article by C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Reviews of Modern Physics 82, 1225–1286 (2010)].
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Berman, P.R. (2018). Scattering: 1-D. In: Introductory Quantum Mechanics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-68598-4_17
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DOI: https://doi.org/10.1007/978-3-319-68598-4_17
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