论文标题
3D非排效量子可促进系统的二次对称代数和光谱
Quadratic symmetry algebras and spectrum of the 3D nondegenerate quantum superintegrable system
论文作者
论文摘要
在本文中，我们介绍了3D非等级的最大量子可整合系统的二次缔合对称代数。这是系统的完整对称代数。证明对称代数包含合适的二次亚词桥，每一个都是由具有相关结构常数的三个发电机生成的，这可能取决于中心元素。我们通过在变形振荡器的背景下对这些亚词法的实现来构建相应的Casimir运算符，并通过这些子代理的实现来呈现有限维的Unirrepers和结构函数。通过对结构函数的约束施加约束，我们获得了3D非整合可整合系统的光谱。我们还表明，该模型是多份的，并且可以在圆柱极和抛物面坐标中的变量分离。我们通过求解系统的schrödinger方程来得出物理谱，并将结果与从代数派生获得的结果进行比较。
In this paper, we present the quadratic associative symmetry algebra of the 3D nondegenerate maximally quantum superintegrable system. This is the complete symmetry algebra of the system. It is demonstrated that the symmetry algebra contains suitable quadratic subalgebras, each of which is generated by three generators with relevant structure constants, which may depend on central elements. We construct corresponding Casimir operators and present finite-dimensional unirreps and structure functions via the realizations of these subalgebras in the context of deformed oscillators. By imposing constraints on the structure functions, we obtain the spectrum of the 3D nondegenerate superintegrable system. We also show that this model is multiseparable and admits separation of variables in cylindrical polar and paraboloidal coordinates. We derive the physical spectrum by solving the Schrödinger equation of the system and compare the result with those obtained from algebraic derivations.
