We reexamine the solvable model problem of two static, fundamental quarks interacting with an SU(2) Yang-Mills field on a spatial circle, introduced by Engelhardt and Schreiber. If the quarks are at the same point, the model exhibits a quantum mechanical supersymmetry. At finite separation, the supersymmetry is explicitly broken in a way which naturally explains the geometrical nature of spectrum and state vectors of this system. [S0556-2821(98)00316-6].