Correlation of particle momenta in quantum-mechanical systems

Correlations of particle momenta in quantum-mechanical systems are studied by considering the expectation values of the cross products of these momenta. Relations between the expectation values of the cross products and squares of particle momenta are derived. In the case of three-particle systems and N-particle systems involving (N - 1) identical particles, these relations make it possible to express the expectation values of the cross products of particle momenta in terms of the expectation values of their squares. The expectation values of the cross products of particle momenta are calculated for three-particle systems with two identical particles from the atomic hydrogen ion H- to the positronium ion e(-)e(-)e(+); for various three-particle systems involving nuclei of helium isotopes, antihydrogen nuclei, muons, and electrons; for various excited states of various three-particle mesic molecules; and for the ground state of the lithium atom.