  We revisit the topic of two-state quantum systems using Geometric Algebra
(GA) in three dimensions $\mathcal G_3$. In this description, both the quantum
states and Hermitian operators are written as elements of $\mathcal G_3$. By
writing the quantum states as elements of the minimal left ideals of this
algebra, we compute the energy eigenvalues and eigenvectors for the Hamiltonian
of an arbitrary two-state system. The geometric interpretation of the Hermitian
operators enables us to introduce an algebraic method to diagonalize these
operators in GA. We then use this approach to revisit the problem of a
spin-$1/2$ particle interacting with an external arbitrary constant magnetic
field, obtaining the same results as in the conventional theory. However, GA
reveals the underlying geometry of these systems, which reduces to the Larmor
precession in an arbitrary plane of $\mathcal G_3$.
