Good quantum number

In quantum mechanics, given a particular Hamiltonian ${\displaystyle H}$ and an operator ${\displaystyle O}$ with corresponding eigenvalues and eigenvectors given by ${\displaystyle O|q_{j}\rangle =q_{j}|q_{j}\rangle }$, then the numbers (or the eigenvalues) ${\displaystyle q_{j}}$ are said to be "good quantum numbers" if every eigenvector ${\displaystyle |q_{j}\rangle }$ remains an eigenvector of ${\displaystyle O}$ with the same eigenvalue as time evolves.

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