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Bulgarian Journal of Physics
Print: 1310-0157 Online: 1314-2666
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RECOGNIZED BY THE EUROPEAN PHYSICAL SOCIETY 
Bulg. J. Phys. vol.51 no.1 (2024), pp. 104-108
Scale Invariant Scattering in 2D
Thomas Curtright1, Christophe Vignat2
1Department of Physics, University of Miami, Coral Gables, FL 33124-8046, USA
2Department of Mathematics, Tulane University, New Orleans, LA 70118z, USA
go back1Department of Physics, University of Miami, Coral Gables, FL 33124-8046, USA
2Department of Mathematics, Tulane University, New Orleans, LA 70118z, USA
Abstract. For a non-relativistic scale invariant system in two spatial dimensions, the quantum scattering amplitude f(θ) is given as a dispersion relation, with a simple closed form for Im f(θ) as well as the integrated cross-section σ ∝ Im f(θ = 0). For fixed θ ≠ 0, the ℏ → 0 classical limit is straightforward to obtain.
doi: https://doi.org/10.55318/bgjp.2024.51.1.104