  We report on the spectroscopic observation of a quantized electronic fine
structure near the Fermi energy in thin Fe films grown on W(110). The quantum
well states are detected down to binding energies of $\sim$10 meV by
angle-resolved photoelectron spectroscopy. The band dispersion of these states
is found to feature a pronounced anisotropy within the surface plane: It is
free-electron like along the $\bar{\Gamma \rm{H}}$-direction while it becomes
heavy along $\bar{\Gamma \rm{N}}$. Density functional theory calculations
identify the observed states to have both majority and minority spin character
and indicate that the large anisotropy can be dependent on the number of
Fe-layers and coupling to the substrate.
