  We investigate the lateral displacement of electronic waves when partially
and totally reflected by a quaternionic potential. Following the analogy
between Quantum Mechanics and Optics we introduce a refractive index for the
complex and the pure quaternionic case. For incidence greater than the critical
one (total reflection) the quaternionic potentials amplify the lateral
displacement found in the complex case. For incidence below the critical angle,
we find, in the quaternionic case, an additional shift. The analytical formula
found for the quaternionic lateral displacement gives the possibility to
observe quantitative and qualitative differences between the complex and
quaternionic Goos-Haenchen shift.

Quantum Physics