The quantization of the energy levels of atomic hydrogen provides many insights into the nature of quantum mechanics. The next four lectures present the basic theory with a slightly heretical spin. The usual power series solution is given, albeit in an unusual form. We will almost get to the famous Bohr formula for the energy states. A picture is worth a thousand words.
Formulas are fine.
The phase-shifts hold the key to all observable quantities in scattering from an isotropic potential. Explicit calculation reveals the connection between the phase shift and the logarithmic derivative of the wavefunction at a distance beyond the range of the short-range potential. Some simple examples. The Scattering Length. The Yukawa Potential in Born Approximation.