The transition rules (or selection rules) describe possible state transitions of a quantum mechanical system, expressed by changes of the quantum numbers. Transition rules exist for various types of quantum numbers:

• Transitions of an electron orbiting an atom.

For the difference between the initial state described by the quantum numbers (n,l,m) and the final state (n',l',m'), the following conditions have to hold:

and

• Vibrational transitions of diatomic molecules. Change of vibrational quantum number v:

• Rotational transitions of molecules. Change of the rotational quantum number J:

The transition rules determine the structure of atomic spectra .