  We solve analytically the energy eigenvalue problem of narrow semiconductor
quantum rings with a general spin-orbit term that includes as a special case
the Rashba and Dresselhaus interactions acting simultaneously. The eigenstates
and eigenenergies of the system are found for arbitrary values of the
spin-orbit coupling constants without making use of approximations. The general
eigenstates are expressed as products of a scalar Mathieu function and a spinor
factor which is periodic or pseudo-periodic on the ring. Our general solution
reduces to the previously found solutions for particular combinations of the
Rashba and Dresselhaus couplings, like the well-studied cases of Rashba-only
and of equal coupling constants.

Mesoscale and Nanoscale Physics;Quantum Physics