Hydrogen Atom

Phase 3: Advanced Quantum Systems

Syllabus Goal

Culmination of potential problems.

The Coulomb Potential

$$ V(r) = -\frac{e^2}{4\pi\epsilon_0 r} $$

Radial Solution

Solutions are Laguerre polynomials. Energy depends only on $n$: $$ E_n = - \frac{13.6 \text{ eV}}{n^2} $$

Wave Functions

$$ \psi_{100} = \frac{1}{\sqrt{\pi a^3}} e^{-r/a} $$ where $a$ is the Bohr radius.