M. I. Haftel

Mixed state quantum mechanics in hydrodynamical form

A newly derive set of quantum fluid dynamical equations appropriate for the description of mixed state dynamics is presented. Based essentially on moments of the Wigner function, the theory presented here uses an expansion of the pseudodistribution function in conjunction with a renormalization technique to obtain a semiclassical approximation for the dynamics of the probability, probability current, and energy densities. Particularly simple equations, ideal fluid dynamics with a nonlocal potential, result from using a local Maxwellian ansatz for the Wigner function. Further, the transformed potential may be easily computed from the fields being convected. Analogies with classical kinetic theory and fluid dynamics are exploited whenever possible.

A time‐dependent variational principle and the time‐dependent Hartree approximation in hydrodynamical form

A quantum mechanical time‐dependent variational principle is generalized using the classical theory of fluids to obtain a variational principle suitable for the fluid dynamical description of mixed state quantum mechanics. A newly derived set of moment equations, in both standard and renormalized form, can be derived with the aid of this principle through minimization of the error in expressing the total derivative of the Wigner function. Coupled systems are studied in the time‐dependent Hartree (TDH) approximation using a novel variational principle, and the renormalization procedure used earlier in the examination of single particle dynamics is extended to the TDH analysis. Use of a local Maxwellian ansatz for each particle results in a particularly simple ‘‘two‐fluid’’ theory, the TDH/LM approximation, which does not violate the standard and renormalized energy conservation theorems derived earlier for the single particle equations. The fluid dynamical TDH/LM approximation is shown to possess a simple ...

Precise non-variational calculation of the μdt molecular ion

Direct solutions of the Schrödinger equation for the ground and excitedS-states of the μdt molecular ion are obtained with the correlation-function hyperspherical-harmonic method. The method generates locally correct wave functions that lead to precise expectation values of the Hamiltonian and of different functions of interparticle distances. The nonlinear correlation factor used in the present work is chosen to provide a proper description of asymptotic behaviour and cusp singularities in all variables. The calculations are compared with our previous CFHH calculations with the linear correlation factor (which accounts only for the μd and μt cusp structure) and with other precision computations. Significant improvements over the linear correlation factor are found, with values of some observables having comparable or better accuracy than in the current literature.