Erratum: Quantum mechanics of a constrained electrically charged particle in the presence of electric currents [Phys. Rev. A 80, 052109 (2009)]

摘要

In our article, we used the following definition of the extrinsic curvature tensor Kij [1] (following the notation in our article): VI l; N/ —Kii. However, in our article, after Eq. (17), the sign of the extrinsic curvature tensor followed the convention V11 iNi = Kii but did not correct for the change in the sign of the extrinsic curvature. When we correct for this missed minus sign, the divergence of the electromagnetic vector potential A in Eqs. (18), (23), and (26) reads V ;1*2A3M)*,(t"11 Ali + 83A3 — where * denotes the wave function and M is the mean curvature in the surface M . If we choose not to fix the electromagnetic gauge, the last term in this expression apparently cancels a corresponding term that appears in the A3 V1* term in the Schrodinger equation. This cancellation apparently removes a possible unphysical contribution to the orbital magnetic moment of the particle. This leaves us with the same expression for the Schrodinger equation in an unfixed electromagnetic gauge as the one in Ref. [2], thus leaving the impression that there is no coupling between curvature and electromagnetic field,