ABSTRACT

Framework for QFD in 3-D Space .............................................................188 12.5 Quantum Fluid Dynamical Equations within a Density Functional

Framework..................................................................................................191 12.6 Miscellaneous Aspects of the Quantum Fluid Dynamical Approach .........193 12.7 Concluding Remarks...................................................................................194 Acknowledgments..................................................................................................194 Bibliography ..........................................................................................................194

The concepts of quantum mechanics (QM) are so radically different from those of classical mechanics that soon after Schrödinger proposed the concept of quantum mechanical wavefunction, there were attempts to provide a classical interpretation of QM. In fact, the success of Madelung [1] in transforming the Schrödinger equation into a pair of hydrodynamical equations consisting of the continuity equation and an Euler type equation of hydrodynamics, giving birth to so-called quantum fluid dynamics (QFD) [2-5], in 1926, itself is testimony to the strong urge to have a classical interpretation of the strange world of QM. The concept was resurrected with full vigor more than 25 years later through the pioneering works of Bohm [6] and Takabayashi [7]. In the meantime, Wigner [8] introduced, in 1932, the concept