Abstract
Via a geometric-capacity-theoretic approach, this note discovers two brand-new formulae for the fractional energy ∫Rn(−Δ)swdν of a quantum particle arising from the fractional Schrödinger-Poisson system(−Δ)sv+(V+w)v=f(⋅,v)&(−Δ)sw=(Γ(s)πn2Γ(n2−s))v2 which models the behavior of a quantum particle within an unknown electrostatic field.
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