论文标题
确切的ChristOffel-Darboux扩展：一种新的，多维的，代数，特征力边界方法
Exact Christoffel-Darboux Expansions: A New, Multidimensional, Algebraic, Eigenenergy Bounding Method
论文作者
论文摘要
尽管Christoffel-Darboux表示（CDR）在正交多项式理论中起着重要作用，并且许多重要的骨髓和费物代性多维Schrodinger方程系统可以转变为矩方程（MER），两者的结合，将两者的结合变成一个有效的，代数，代数，eigegraic，eigeigenergy的界面，却遍布界限。这两种表示的特殊融合（适用于边界的骨器或费米子系统）定义了此处开发的正顺式多项式投影量化 - 边界方法（OPPQ -BM）。我们使用它来分析几个维度和二维系统，包括用于强苏普斯特朗磁场的二次Zeeman效应。对于这个问题，我们在不需要任何截断或近似值的情况下匹配或超过了Kravchenko等人（1996Phys。Rev。A 54287）的出色但复杂的结果。
Although the Christoffel-Darboux representation (CDR) plays an important role within the theory of orthogonal polynomials, and many important bosonic and fermionic multidimensional Schrodinger equation systems can be transformed into a moment equation representation (MER), the union of the two into an effective, algebraic, eigenenergy bounding method has been overlooked. This particular fusion of the two representations, suitable for bounding bosonic or fermionic systems, defines the Orthonormal Polynomial Projection Quantization - Bounding Method (OPPQ-BM), as developed here. We use it to analyze several one dimensional and two dimensional systems, including the quadratic Zeeman effect for strong-superstrong magnetic fields. For this problem, we match or surpass the excellent, but intricate, results of Kravchenko et al (1996 Phys. Rev. A 54287) for a broad range of magnetic fields, without the need for any truncations or approximations.
