We study wave equations with energy dependent potentials. Simple analytical models are found useful to illustrate difficulties encountered with the calculation and interpretation of observables. A formal analysis shows under which conditions such equations can be handled as evolution equation of quantum theory with an energy dependent potential. Once these conditions are met, such theory can be transformed into ordinary quantum theory.

The energy-density formalism is applied to finite nuclei. The total energy of the many-nucleon system is expressed as a functional E{p) of the local density p (r), and the ground-state density distribution is found by minimization with respect to p(r). The functional of the potential energy is directly derived from a nuclear-matter calculation with variable neutron excess by Brueckner et al. The density-gradient correction which takes care of the density variation at the nuclear surface contains an exchange-and a correlationenergy part. In a first attempt, proton and neutron densities are assumed proportional; therefore the present calculation is limited to light nuclei. The density distributions are found to be of the so-called modified Gaussian type with a cubic polynomial. Binding energy, radius, and surface thickness are in good agreement with experiment.

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