This monograph tackles three challenges. First, show math that matches known elementary particles. Second, apply the math to match other known physics data. Third, predict future physics dataThe math features solutions to isotropic pairs of isotropic quantum harmonic oscillators. This monograph matches some solutions to known elementary particles. Matched properties include spin and types of interactions in which the particles partakeOther solutions point to possible elementary particlesThis monograph applies the math and the extended particle list. Results narrow gaps between physics data and theory. Results pertain to elementary particles, astrophysics, and cosmologyFor example, this monograph predicts properties for beyond-the-Standard-Model elementary particles, proposes descriptions of dark matter and dark energy, provides new relationships between known physics constants, includes theory that dovetails with the ratio of dark matter to ordinary matter, includes math that dovetails with the number of elementary-fermion generations, and suggests forces that govern the rate of expansion of the universe.