This result diverges when no limits about the integral (at both large and small frequencies). As mentioned above, this method is expected to be valid only when ν ν > π π c / a 0 , or equivalently k > π π / a 0 . It is also valid only for wavelengths longer than the Compton wavelength, or equivalently k < m c / ℏ ℏ . Therefore, one can choose the upper and lower limit of the integral and these limits make the result converge.