In the spirit of the preceding discussion on geometric potentials, we extend the same to the realm of atomic matter where we base our understanding of quantum mechanics constructed from geometric fields instead of the 1/r electrostatic potentials. The 1/r potentials have been used to study atoms since the conception of quantum mechanics, however we will reintroduce the theory with geometric fields here. Results show that these geometric fields preserve the duality of attractive (nuclear-electronic) and repulsive (nuclear-nuclear and electronic-electronic) potentials encountered in atoms, with a complete spectrum of solvable eigenvalue problems - the way they are solved in conventional quantum mechanics. The previously visited wave equations in previous articles, can now be extended to resolve the Schrodinger wave equation for nuclei and electrons to render the complete picture of atomic matter. Specifically, we discuss geometric potentials analogous to the quantum harmonic oscillator problem and study natural extensions to higher order harmonic oscillators. This is essential if one wants to deduce the exact wavefunctions of atoms and molecules in isolated and lattice systems alike.