Exact Christoffel-Darboux expansions: A new, multidimensional, algebraic, eigenenergy bounding method

Although the Christoffel-Darboux representation (CDR) plays an important role within theory of orthogonal polynomials, and many bosonic fermionic multidimensional Schrodinger equation systems can be transformed into a moment (MER), union two effective, algebraic, eigenenergy bounding method has been overlooked. This particular fusion representations, suitable for or systems, defines Orthonormal Polynomial Projection Quantization - Bounding Method (OPPQ-BM), as developed here. We use it to analyze several one dimensional including quadratic Zeeman effect strong-superstrong magnetic fields. For this problem, we match surpass excellent, but intricate, results Kravchenko et al (1996 Phys. Rev. A 54287) broad range fields, without need any truncations approximations.