“…In a previous work [6] the Schrodinger equation for an electron on a toroidal surface T 2 in an arbitrary static magnetic field was developed and numerical results obtained. There however, the electron was restricted ab-initio to motion on T 2 , which precluded the appearance of the well known geometric potential V C ∝ (h 2 − k), [26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42] with h, k the mean and Gaussian curvatures, that arises via thin-layer quantization [43]. Furthermore, if the degree of freedom normal to Σ (labelled q in everything to follow) is included, then the component of the vector potential A N normal to Σ couples to the normal part of the gradient.…”