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Non-relativistic and relativistic scattering by short-range potentials.
H Arnbak1, P L Christiansen, Yu B Gaididei
1Department of Informatics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark.
Summary
This study explores relativistic and non-relativistic scattering using regularization techniques for short-range potentials. It reveals resonant penetration and non-unique scattering coefficients, with detailed analysis of non-relativistic approximations.
Area of Science:
- Quantum mechanics
- Mathematical physics
Background:
- Scattering theory is fundamental to understanding particle interactions.
- Short-range potentials present unique challenges in relativistic and non-relativistic quantum mechanics.
Purpose of the Study:
- To investigate relativistic and non-relativistic scattering by short-range potentials.
- To explore the application of regularization techniques for solving scattering problems.
- To analyze the behavior of scattering coefficients and resonant phenomena.
Main Methods:
- Utilized a perturbation technique with a stretched variable for regularization.
- Solved scattering problems involving the delta prime potential (Schrödinger equation) and delta potentials (Dirac equation).
- Investigated asymmetric regularizations and their impact on scattering coefficients.
Main Results:
- Demonstrated resonant penetration through short-range potentials.
- Identified non-unique scattering coefficients arising from asymmetric regularizations.
- Provided a detailed discussion of approximate Schrödinger equations in the non-relativistic limit.
Conclusions:
- Regularization techniques, particularly with a stretched variable, are effective for scattering problems with short-range potentials.
- The choice of regularization method can influence scattering outcomes, leading to non-uniqueness.
- Understanding non-relativistic limits is crucial for a complete picture of scattering phenomena.
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