Abstract
The logarithmic convexity or concavity of a ground state wave function divide by a comparison function is an essential tool in deriving theorems on level ordering and inequalities for scattering phase shifts. The simple proof which Martin gave for comparison with Coulomb systems is generalized in two ways. The logarithmic convexity property can now be proved in a simple way also in comparison with other systems, not only the hydrogen atom, and for functions which are solutions of the Schrödinger equation but not square integrable.
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