ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Properties of "mixed moments,'' 〈r μ〉l,L≡∫∞0r μuL (r)ul(r)dr of ground state wave functions ul(r) of angular momentum l are investigated. It is shown that for cases where the Laplacian of the central potential V(r) is positive (negative), 〈r μ〉l,L/Γ(μ+L+l+3) is a concave (convex) function of μ. These results are extended to other classes of potentials and inequalities relating "mixed moments'' to "standard moments'' with L=l, are derived. The latter are used to give a simpler, more comprehensive proof of convexity (concavity) properties of the ground state energies E(0,l) as functions of l. New rigorous bounds on the overlap 〈1〉l,L of two angular momentum ground states, the mean square radius and kinetic energies of ground states and the electric dipole moment for transition rates between two such states are obtained for various classes of potentials using the above "moment'' inequalities. These bounds are tested in the framework of a recent potential model description of the upsilon system.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.529058
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