  The triumph of effective mass theory in describing the energy spectrum of
dopants does not guarantee that the model wavefunctions will withstand an
experimental test. Such wavefunctions have recently been probed by scanning
tunneling spectroscopy, revealing localized patterns of resonantly enhanced
tunneling currents. We show that the shape of the conducting splotches resemble
a cut through Kohn-Luttinger (KL) hydrogenic envelopes, which modulate the
interfering Bloch states of conduction electrons. All the non-monotonic
features of the current profile are consistent with the charge density
fluctuations observed between successive {001} atomic planes, including a
counterintuitive reduction of the symmetry - a heritage of the lowered point
group symmetry at these planes. A model-independent analysis of the diffraction
figure constrains the value of the electron wavevector to $k_0 = (0.82 \pm
0.03)(2\pi/a_{Si})$. Unlike prior measurements, averaged over a sizeable
density of electrons, this estimate is obtained directly from isolated
electrons. We further investigate the model-specific anisotropy of the wave
function envelope, related to the effective mass anisotropy. This anisotropy
appears in the KL variational wave function envelope as the ratio between Bohr
radii b=a. We demonstrate that the central cell corrected estimates for this
ratio are encouragingly accurate, leading to the conclusion that the KL theory
is a valid model not only for energies but for wavefunctions as well.
