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The hydrogenic Schrödinger solution provides wavefunctions for a single electron in a Coulomb potential. The principal, orbital angular momentum, and magnetic quantum numbers specify allowed states and describe their energy, shape, and orientation. For a given principal quantum number, the ideal energy depends only on that number, while probability densities, nodes, and radial distributions describe the spatial structure. Transitions between levels give characteristic spectral lines and obey electric-dipole selection rules. External electric and magnetic fields, along with fine and hyperfine interactions, add further structure. The lesson also connects orbital size and ionization to expectation values and introduces the virial theorem and the role of hydrogenic wavefunctions as a basis for more complex atomic calculations.