  The OH molecule is currently of great interest from the perspective of
ultracold chemistry, quantum fluids, precision measurement and quantum
computation. Crucial to these applications are the slowing, guiding,
confinement and state control of OH, using electric and magnetic fields. In
this article, we show that the corresponding eight-dimensional effective ground
state Stark-Zeeman Hamiltonian is exactly solvable and explicitly identify the
underlying chiral symmetry. Our analytical solution opens the way to insightful
characterization of the magnetoelectrostatic manipulation of ground state OH.
Based on our results, we also discuss a possible application to the quantum
simulation of an imbalanced Ising magnet.
