What has Quantum Chemistry Got to Do with It?

Abstract

The time has come to see how the concept of irreducible representations ties in with quantum chemistry. After a brief introduction to the prequantum principles of symmetry, we will show that eigenfunctions of the Hamiltonian are also eigenfunctions of the symmetry operators that commute with the Hamiltonian. We further analyze the concept of a degeneracy and show how the degenerate components can be characterized by canonical symmetry relationships. The final section will then provide a detailed account of the symmetry operations that leave the Hamiltonian invariant.