Abstract
We study the non-relativistic quantum mechanical scattering problem of a plane-wave by a Chebyshev particle in two spatial dimensions. The Chebyshev particle is a wavy, or undulating, circle. We formulate the problem using the Lippmann–Schwinger (LS) equation and the Chebyshev particle as a boundary-wall potential. This potential is naturally symmetric as a function of the so-called undulation parameter, and we use these symmetries to solve the LS equation and calculate three important physical quantities: the differential cross-section, the total cross-section and the quantum refractive index. We analyze these quantities as functions of the wave number k, the coupling strength γ as well as the undulation and deformation parameters of the Chebyshev particle.
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