  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.
