Evolution of a Quantum System: Lifetime of a Determinant

A measure of the "dependency" of a many-particle system is defined and its time dependence is evaluated for systems initially described by a single Slater determinant. An uncertainty product between the energy spread of the initial determinant and the lifetime of a system's independence is established. Numerical estimates of some lifetimes are given. They are not so long as to be reassuring for nuclear time-dependent Hartree-Fock calculations. Each separate case ought to be checked.