One of the most important tasks of a future linear collider is the
precise measurement of the threshold production cross section of top
quark pairs. In order to match the expected experimental precision
it is necessary to perform theoretical predictions which include
corrections up to third order in perturbation theory. In this contribution
we report about the corrections of order $\beta_0^3\alpha_s^3$ to the
heavy quark spectrum and wave function. Physical applications both for
the top and bottom quark system are discussed.
