very few relatively simple model Hamiltonians quantum harmonic oscillator particle in a box dihydrogen cation hydrogen atom helium electron Hamiltonian Schrödinger equation atom electrons
Analytic solutions of the Schrödinger equation are known for very few relatively simple model Hamiltonians including the quantum harmonic oscillator, the particle in a box, the dihydrogen cation, and the hydrogen atom. Even the helium atom – which contains just two electrons – has defied all attempts at a fully analytic treatment.
