Fluid Dynamics (or Bohmmian) Representation of the Schrodinger, Nonlinear Schrodinger and the Davey-Stewart equations
主 题: Fluid Dynamics (or Bohmmian) Representation of the Schrodinger, Nonlinear Schrodinger and the Davey-Stewart equations
报告人: Attila Askar 土耳其数学会理事长 (Koç University)
时 间: 2016-12-12 15:00-16:00
地 点: 理科一号楼1303
This approach is partly motivated by Einstein’s questioning of the completeness of the quantum theory that is dramatized by his famous statement: “God doesn’t throw dice” while admitting to its internal consistency while admitting to its internal consistency. The QFD representation has its foundations in Bohm’s interpretation of quantum mechanics with the goal to find classically identifiable dynamical variables at the sub-particle level. The approach leads to two conservation laws, one for “mass” and one for “momentum”, similar to those in hydrodynamics for a compressible fluid with a particular constitutive law. The QFD equations are a set of nonlinear partial differential equations. In this sense, they may be seen as a step in the negative direction as compared to the linear Schrodinger equation. However, in this scheme, the oscillatory real and imaginary components of the complex wave function are replaced by the monotonous the amplitude and phase. This may be exploited as a significant advantage in computational quantum mechanics. Moreover, the nonlinear field equations are also suggested as the natural framework for studying fundamentally nonlinear phenomena such as solitons and chaos. This paper shows results with the Schr?dinger equation for dissociation problems and extends the QFD formalism of quantum mechanics to the Nonlinear Schrodinger or the Gross-Privestiki equation and the Davey-Stewardson equations. Several invariants of the solution are derived for the n-dimensional version of these equations.