Perturbed Coulomb Problems via SO(2,1) Algebra
So far, we have not solved many perturbed Coulomb problems by conventional perturbation theory, that is, by the conventional radial and angular functions. The difficulty here is that perturbation terms which are functions of the radial coordinate, r, lead to an infinite number of nonzero matrix elements, connecting a bound state of definite, n, to all other bound states, as well as to the full spectrum of continuum states. The complete set of states includes both the bound states and the continuum states.
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