Quantum fluid dynamics of many-electron systems in three-dimensional space



In presence of external electric and magnetic fields, the Schrödinger equation for many-electron systems is transformed into a continuity equation and an Euler-type equation of motion in configuration space. Then, using the natural-orbital Hamiltonian, as defined by Adams, the two fluid-dynamical equations are derived in the three-dimensional space. This generates a “classical” view of such quantum systems, corresponding to an MCSCF wave function: The many-electron Schrödinger fluid consists of individual fluid components, each corresponding to a natural orbital and having its own charge density and current density. The local observables, viz., the net charge density and net current density, are obtained by merely summing over the natural orbitals, with the occupation numbers as weight factors; but, the net velocity field cannot be so obtained. Further, although each fluid component moves irrotationally in the absence of a magnetic field, the net velocity field is not irrotaional. The irrotational character of each velocity component is destroyed by rotation of the nuclear framework of the system while electron spin introduces an additional term, the spin magnetization moment, into each component current density. The physical significance of the fluid-dynamical equations as well as their advantages and disadvantages are discussed.