Refining the general comparison theorem for the Klein–Gordon equation

By recasting the Klein–Gordon equation as an eigen-equation in coupling parameter [Formula: see text] basic comparison theorem may be written text], where and are monotone nondecreasing shapes of two central potentials on text]. Meanwhile, corresponding parameters that functions energy We weaken sufficient condition for ground-state spectral ordering by proving (for example dimension) if couplings remain ordered ground-states corresponding, respectively to a given This result is extended spherically symmetric radial dimensions.