Separation of electronic and nuclear motions and the dynamical Schrödinger group.

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A new approach to the separation of electronic and nuclear motions in the molecular and solid-state quantum mechanics is proposed that accounts for the finite velocity of an electron and its retardation in following the nuclear motions. Such a retarded nuclear coordinate transforms the Hamiltonian of the harmonic oscillator into the linear combination of operators forming the Lie algebra of the dynamical Schr\"odinger group. The time evolution of these operators defines the local time for nuclear and electronic motions. An electronic pair in the same local time has a lower value of the ground energy and a nonvanishing value of the group velocity and electronic current density.