BOUND-STATES IN TUBULAR QUANTUM WAVE-GUIDES WITH TORSION

We consider a quantum particle constrained to move within a tube of ce ntral radius d embedded in 3-space, subject to Dirichlet boundary cond itions. Taking the central axis of the tube as a reference curve and s etting up a locally cylindrical polar coordinate system around this cu rve, we derive an exact expression for the effective potential introdu ced by the imposition of curvature and torsion. We then employ a minim ax method to ascertain a sufficient requirement for the curvature and torsion to guarantee the existence of a bound state.