The Yukawa and Hulthen potentials in quantum mechanics

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Abstract
The concept of kinetic potentials is used to construct a global geometrical approximation theory for the spectra of Schrodinger operators H=- Delta +vy in which the potential shape y is either (i) a transformation y(r)=g(h(r)) of a soluble potential h(r) or (ii) a continuous mixture y(r)= integral rho (t)h(rt) dt. The case in which y is the Yukawa potential and h=-(er-1)-1 is the Hulthen potential is discussed in detail. Simple formulae are derived for eigenvalue bounds which are compared to accurate data obtained by the direct numerical integration of Schrodinger's equation.