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Entropy on charge density: making the quantum mechanical connection.

Entropy maximization has proven effective in treating certain aspects of the phase problem of X-ray diffraction. Much of its development has been expressed in probabilistic language, although image enhancement has been somewhat more physical or geometric in description. Here phasing and entropy maximization are embedded in the quantum mechanical problem of reconstructing an electronic one-matrix under experimental constraints. Entropy on an N-representable one-particle density matrix is well defined. The entropy is the expected form, and it is a simple function of the one-matrix eigenvalues which all must be non-negative. Certain other properties are pertinent to phasing which is implicit in one-matrix reconstruction governed by entropy maximization. Throughout this work reference is made to informational entropy, not the entropy of thermodynamics.