2024/06/05 by Eduardo V. S. Anjos, Antonio C. Pavão, Antônio C. Pavão +6
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Topological Materials and Phenomena #Cold Atom Physics and Bose-Einstein Condensates
paper · pdf · doi:10.1007/s00894-024-06030-y
Abstract 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 \varvecπ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> </mml:math> electrons in polyenes, we follow two approaches. First, we utilize a weakened Coulomb potential associated with a spiral curve. The solution to the Schrödinger equation with Dirichlet boundary conditions yields Bessel functions, and the spectrum is obtained analytically. We employ the particle-in-a-box model in the second approach, incorporating effective mass corrections. The \varvecπ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> </mml:math> - \varvecπ * <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>π</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> transitions of polyenes were calculated in good experimental agreement with both approaches, although with different wave functions.