Using Kaluza-Klein theory we study the quantum mechanics of a scalar partic
le in the background of a magnetic cosmic string and in the background of a
chiral cosmic string. We show that the wave functions, the phase shifts, a
nd scattering amplitudes associated with the particle depend on the global
features of those spacetimes. These dependences represent gravitational ana
logues of the well-known Aharonov-Bohm effect. In addition, we discuss the
Landau levels in the presence of a cosmic string in the framework of Kaluza
-Klein theory. [S0556-2821(99)03610-3].