Quantum mechanics of particles constrained to spiral curves with application to polyene chains.

Context: Due to advances in synthesizing lower-dimensional materials, there is the challenge of finding the wave equation that effectively describes quantum particles moving on 1D and 2D domains. Jensen and Koppe and Da Costa independently introduced a confining potential formalism showing that the effective constrained dynamics is subjected to a scalar geometry-induced potential; for the confinement to a curve, the potential depends on the curve's curvature function.

Method: To characterize the electrons in polyenes, we follow two approaches.