# Path-integral Riemannian contributions to nuclear Schrodinger equation

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## Abstract

%A L. Ingber %T Path-integral Riemannian contributions to nuclear Schro¨dinger equation %J Phys. Rev. D %V 29 %P 1171-1174 %D 1984 Path-integral Riemannian contributions to nuclear Schr¨odinger equation Lester Ingber Physical Studies Institute, Drawer W, Solana Beach, California 92075 and Institute for Pure and Applied Physical Sciences, University of California San Diego, La Jolla, California 92093 (Received 28 July 1983) Several studies in quantum mechanics and statistical mechanics have formally established that non- flat metrics induce a difference in the potential used to define the path-integral Lagrangian from that used to define the differential Schr¨odinger Hamiltonian. A recent study has described a statistical mechanical biophysical system in which this effect is large enough to be measurable. This study demonstrates that the nucleon-nucleon velocity-dependent interaction derived from meson exchanges is a quantum mechan- ical system in which this effect is also large enough to be measurable. PA CS numbers 1983: 13.75.Cs, 03.65.Db, 21.30.+y, 02.50.+s I. INTRODUCTION In the last few years, several investigators have noted that the potential contribution in the differen- tial Hamiltonian operator of the Schr¨odinger equation differs from the corresponding potential contribu- tion to the path-integral Lagrangian, when the metric is non-flat [1-10]. Similar differences occur in sta- tistical mechanics, between the differential Fokker-Planck equation and the Onsager-Machlup Lagrangian, extended to systems with nonlinear drift and nonconstant diffusion [11-14]. All these authors have noted that these differences are as yet untested, in that these Riemannian ‘‘corrections’’ are too small to be measurable in most physical systems. However, recently a statistical mechanical system, the statistical mechanics of neocortical interactions [15,16], has been shown to possess such corrections that are large enough to be measurable within ranges of current empirical values of synapti

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