Abstract
Most two-particle interaction potentials V (x 1 − x 2) assume a finite value V ∞ if | x 1 − x 2 | → ∞. If the relative motion of the two-particle system has an energy E > V ∞ the particles can have arbitrary large distance. In particular, we can imagine a situation where the two particles approach each other from an initially large separation and after reaching some minimal distance move away from each other. The force between the two particles will influence the trajectories of the two particles, and this influence will be strongest when the particles are close together. The deflection of particle trajectories due to interaction forces is denoted as scattering. This is denoted as potential scattering if the interaction forces between the particles can be expressed through a potential.
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Notes
- 1.
E. Schrödinger, Annalen Phys. 385, 437 (1926).
- 2.
Please note that the definition used here differs by factors of 2 from the definition used by Schrödinger, \({\lambda }_{1} \equiv {\xi }_{S} = 2\xi \), \({\lambda }_{2} \equiv {\eta }_{S} = 2\eta \).
- 3.
W. Gordon, Z. Phys. 48, 180 (1928).
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Dick, R. (2012). Scattering Off Potentials. In: Advanced Quantum Mechanics. Graduate Texts in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8077-9_11
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