Lecture 1
Physical systems we'll study: real atoms, artificial atoms like superconducting qubits, quantum dots, etc.
Hydrogen system, take the standard soln of the Schrodinger equation with only p^2/2m - e^2/r, you get the standard $E_n = \frac{13.6 eV}{n^2}$, and here theres' a ton of degeneracy.  Atomic structure is characterized by quantum numbers, which are associated with some conservation law or symmetry.  Standard argument: say $