SPECTRAL-MOMENT CONSTRAINED BOUNDS FOR ABSOLUTE MAXIMA OF SINGLE-PARTICLE PROBABILITY DENSITIES OF EXCESS ELECTRONS

Rigorous lower and upper bounds are derived for the single-particle absolute density maxima of excess electrons. These bounds are expressed solely in terms of the dispersion in position and the dispersion in momentum of a typical electron, which are directly determinable from the pertinent spectral moments of the electron's measured absorption spectrum. The bounds obtained enable estimates to be made of absolute density maxima that are far better than within an order of magnitude of the actual values.