Exact Solutions to Schrödinger Equation for a Charged Particle on a Torus in Uniform Electric and Magnetic Fields

Abstract

We present exact solutions of the Schrödinger equation for a charged particle constrained to move along a toroidal surface in the presence of uniform electric and magnetic fields.

Quantum particle on a surface: Catenary surface and Paraboloid of revolution

“…In [12] the authors studied the an electron on a catenoid surface. Oliveria et al in [13] solved the Schrödinger equation on a sphere under non-central potential and Schmidt in [14] and [15] introduced exact solutions of Schrödinger equation for a charged particle confined on a sphere, on a cylinder and on a torus while is imposed with uniform electric and magnetic fields. Furthermore, electrons confined on a rotating sphere in the presence of a magnetic field has been considered by Lima et al in [16] and the effects of the rotation was compared with the effects of the magnetic fields.…”

Magnetic and geometric effects on the electronic transport of metallic nanotubes

“…They extended the da Costa approach [46], which reveals an effective geometric potential due to curvature, to include an externally applied electromagnetic field. Their approach has been applied to the study of charged particles on a variety of surfaces under applied electromagnetic fields [47][48][49][50]. Here, we study the effects of a magnetic field in the electronic transport of deformed nanotubes.…”