We discuss the possible observable consequences of the incorporation of Dirac monopole in quantum mechanics. Particularly, we consider the selection rules of dipole transitions and the Stark effect for the hydrogen atom with non-zero magnetic charge.Then we discuss similar problems in the systems with arbitrary central potentials and position-dependent masses. Finally, we propose the integrable system describing the motion of the probe particle in the field of two fixed dyons (electrically charged monopoles) and show that in the limiting case it results in the hydrogen atom interacting with parallel homogeneous electric and magnetic fields plus special potential field.