 Mass-radius scaling of confinement energy

If mass m, confinement radius R and Planck constant h are the only dimensional inputs to a nonrelativistic kinetic energy, matching mass, length and time dimensions gives $K=C{h}^2/(m{R}^2)$. The dimensionless coefficient C depends on the boundary condition and state. Ratios of energies therefore scale as inverse mass and inverse radius squared only when that dimensionless physics is unchanged. This separates a robust scaling law from a claim about an unspecified confinement spectrum.