We analyze the single-particle quantum mechanics of an atom whose dispersion is modified by spin-orbit coupling to Raman lasers. Such a setup can create a double-well-shaped dispersion, which leads to unusual single-particle physics. We show how this dispersion influences the symmetry of the ground-state wave function in different physical-space potentials, including a square well, a harmonic well, and a double well. © 2012 American Physical Society.