Exact solutions of Schrodinger equation for a charged particle on a sphere and on a cylinder in uniform electric and magnetic fields

We present exact solutions for the Schrodinger equation in the presence of uniform electric and magnetic fields for two distinct surfaces: spherical and cylindrical. For the spherical geometry we solve the generalized spheroidal equation - using a series of associated Legendre functions when both fields are present; and spheroidal functions Ps(theta,phi) for the case where there is only a magnetic field - and study the time-evolution of a gaussian wavepacket. The revival effect takes place exactly at 2 pi. For the cylindrical geometry we manage to solve the Schrodinger equation for a magnetic field pointing off the symmetry axis, namely B = B(1)i + B(o)k and an electric field E = epsilon(0)j. The eigenfunctions are written as products of plane waves, in z-direction, and solutions of Ince equation with complex parameters xi and p.