Comment on “Quantum mechanics of an electron in a homogeneous magnetic field and a singular magnetic flux tube”

Recently Thienel [Ann. Phys. (N.Y.) 280 (2000), 140] investigated the Pauli equation for an electron moving in a plane under the influence of a perpendicular magnetic field which is the sum of a uniform field and a singular flux tube. Here we criticise his claim that one cannot properly solve this equation by treating the singular flux tube as the limiting case of a flux tube of finite size. Typeset using REVTEX ∗E-mail:[email protected] 1 The Pauli Hamiltonian for an electron (of mass M , charge −|e| and g-factor 2) moving in the (x, y)-plane under the influence of a magnetic field pointing in the z-direction is given by H = 1 2M ( p+ |e| c A )2 + |e|h̄ Mc BzSz. (1) Thienel [1] has recently investigated the eigenvalue problem for this Hamiltonian in the case of a magnetic field which is the sum of a uniform field and a singular flux tube, Bz(r) = B + αΦδ (r) (B > 0; Φ ≡ 2πh̄c/|e|) . (2) He claims that standard approaches to this problem fail. The purpose of this Comment is to show not only that they do work, they are also simpler than his alternative method. As Thienel, we choose the vector potential in the symmetric gauge, A(r) = ( Br 2 + αΦ 2πr ) eφ, and use magnetic units (where the unit of length is λ = (Φ/πB) and the unit of energy is h̄ω, with ω = |e|B/Mc the Larmor frequency). Then we can rewrite (1) as H = − 1 4r ∂ ∂r (