Bohm Aharonov effect : Consider a YDSE experiment done with electrons
The debroglie hypothesis says that electrons behave like waves and so in presence of double slit, they show interference pattern as shown by dotted line. But if we introduce a thin strip (w < < L) of magnetic field just in front of slits, the electrons trajectory would bend by a small angle and so the central maxima shifts up by a distance $\Delta y.$ This shift can be easily shown to depend on magnetic field B, charge q, width w, the momentum of electron p, slit distance d and L. The same result can be derived using principles of quantum mechanics. In quantum mechanics we cannot talk about definite path. So we cannot talk about bending of electron trajectory. There it is found that on passing through the region of magnetic field, the electrons waves undergo a phase change. So the electrons wave coming from upper slit and that from lower slit have a phase difference. Interestingly the path difference resulting from this phase difference predicts the same shift of central maxima $\Delta y$ as does the classical theory using magnetism