Good quantum number
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In quantum mechanics, the eigenvalue of an observable is said to be a good quantum number if the observable is a constant of motion. In other words, the quantum number is good if the corresponding observable commutes with the Hamiltonian. If the system starts from the eigenstate with an eigenvalue , it remains on that state as the system evolves in time, and the measurement of always yields the same eigenvalue .[1]
Good quantum numbers are often used to label initial and final states in experiments. For example, in particle colliders:[citation needed]
- Particles are initially prepared in approximate momentum eigenstates; the particle momentum being a good quantum number for non-interacting particles.
- The particles are made to collide. At this point, the momentum of each particle is undergoing change and thus the particles’ momenta are not a good quantum number for the interacting particles during the collision.
- A significant time after the collision, particles are measured in momentum eigenstates. Momentum of each particle has stabilized and is again a good quantum number a long time after the collision.