To make equations of the previous section applicable to the states belonging to the continuum spectrum, they should be rewritten in terms of matrix elements of the momentum . In absence of magnetic field, the Hamiltonian can be written as , and calculating a commutator  in the basis of eigenfunctions of  results in the relation between matrix elements
Next, calculating matrix elements of a commutator  in the same basis and eliminating matrix elements of , we arrive at
Because , the above expression results in a sum rule
where  are oscillator strengths for quantum transitions between the states  and . This is the Thomas-Reiche-Kuhn sum rule, and the term with  has been omitted because in confined systems such as atoms or molecules the diagonal matrix element  due to the time inversion symmetry of the Hamiltonian . Excluding this term eliminates divergency because of the vanishing denominator.