It is observed that the in and out states of a particle of energy k 2/2m, entering or leaving a Coulomb field along the +z direction, are eigenstates of L3 with eigenvalue 0, and of A3, the third component of the Runge-Lenz vector, with eigenvalues ±αx+ik/m, respectively. From this characterization and the commutation relations of the symmetry group, the phase shifts are easily obtained algebraically.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics