Local coordinate, wave vector, Fisher and Shannon information in momentum representation

The formalism of Luo [Int. J. Theor. Phys. 41 (2002) 1713] on local values of quantum observables is generalized for N-electron systems both in coordinate and momentum spaces. It is shown that the imaginary part of the total local coordinate (momentum) is the half of the local wave vector (or the half of the gradient of the local momentum(coordinate)-space Shannon information per particle).

► We studied total local momentum and coordinate for N-electron systems.
► The total local momentumʼs imaginary part is the half of the local wave vector.
► The total local coordinateʼs imaginary part is half of Shannon entropyʼs gradient.