Commutation Memes

Finding a Hermitian operator that commutes with the Hamiltonian is like striking quantum gold—it gives you those sweet, sweet conserved quantities. But the moment you're dealing with degenerate states, you start eyeing that operator like it's your ex who just texted "we need to talk." Suddenly, perturbation theory looks mighty attractive. For the uninitiated: Hermitian operators represent physical observables in quantum mechanics. When one commutes with the Hamiltonian (H), it means you can measure both properties simultaneously—a rare luxury in the quantum world. Degenerate states, however, are quantum mechanics' way of saying "it's complicated."