  The excitation spectrum of the frustrated spin-$1/2$ Heisenberg chain is
reexamined using variational and exact diagonalization calculations. We show
that the overlap matrix of the short-range resonating valence bond states basis
can be inverted which yields tractable equations for single and two spinons
excitations. Older results are recovered and new ones, such as the bond-state
dispersion relation and its size with momentum at the Majumdar-Ghosh point are
found. In particular, this approach yields a gap opening at $J_2=0.25J_1$ and
an onset of incommensurability in the dispersion relation at $J_2=9/17J_1$ [as
in S. Brehmer \emph{et al.}, J. Phys.: Condens. Matter \textbf{10}, 1103
(1998)]. These analytical results provide a good support for the understanding
of exact diagonalization spectra, assuming an independent spinons picture.
