  Topological insulators in three dimensions are studied as a problem of
supersymmetric quantum mechanics. The spin-orbit coupling is induced as a
consequence of the supersymmetrization procedure and we show that it is
equivalent to the appearance of a $SU(2)$ connection. The procedure presented
in this letter is general and valid for any three-dimensional quantum system.
The approach allows -- in principle -- to study a wide range of topological
insulators as standard quantum mechanical problems. As an illustration the
three-dimensional harmonic oscillator and the Aharonov-Bohm effect are studied
in detail.
