  The description of the electron wavefunctions in atoms is generalized to the
fractional Fourier series. This method introduces a continuous and infinite
number of chirp basis sets with linear variation of the frequency to expand the
wavefunctions, in which plane-waves are a special case. The chirp
characteristics of each basis set can be adjusted through a single parameter.
Thus, the basis set cutoff can be optimized variationally. The approach is
tested with the expansion of the electron wavefunctions in atoms, and it is
shown that chirp basis sets substantially improve the convergence in the
description of the electron density. We have found that the natural
oscillations of the electron core states are efficiently described in
chirp-waves.
