论文标题
在谐波振荡器存在下，在螺旋形表面上的量子颗粒运动
Quantum particle motion on the surface of a helicoid in the presence of harmonic oscillator
论文作者
论文摘要
量子力学中的几何潜力最近引起了人们的关注，从而提供了一种形式主义，以研究低维系统中曲率的影响。在本文中，我们研究了用于各向异性质量张量的Schrödinger方程中的螺旋形几何形状的后果。特别是，在这种情况下，我们解决了谐波振荡器的问题。我们根据汇合的HEUN功能确定本征函数并计算各自的能级。该系统表现出几种不同的行为，具体取决于质量成分的调整。
The geometric potential in quantum mechanics has been attracted attention recently, providing a formalism to investigate the influence of curvature in the context of low-dimensional systems. In this paper, we study the consequences of a helicoidal geometry in the Schrödinger equation dealing with an anisotropic mass tensor. In particular, we solve the problem of an harmonic oscillator in this scenario. We determine the eigenfunctions in terms of Confluent Heun Functions and compute the respective energy levels. The system exhibit several different behaviors, depending on the adjustment on the mass components.
