On the relationship between the one-electron and Bohm's quantum potential

The one-electron potential, derived from the electron density, is a three-dimensional function, whereas Bohm's quantum potential depends on the spatial coordinates of all involved electrons. To analyze the relationship between the two potentials in the many-electron case, first the dimensionality of the quantum potential needs to be reduced to match that of the one-electron potential. A possible approach for such dimensionality reduction by calculating the expectation value of the quantum potential over all but one electron, using the factorization of the real part of the wave function into a marginal and conditional function is presented, and a relation between such three-dimensional local quantum potential and the one-electron potential is given.(C) 2002 John Wiley Sons, Inc.