A center-of-mass principle for the multiparticle Schrödinger equation

Semiclassical Solutions of the Nonlinear Schrödinger Equation

A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schrödinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass of such a solution is shown to move along with the bicharacteristics of the basic symbol of the corresponding linear Schrödinger equation. The leading term of...

Schrödinger equation from an exact uncertainty principle

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrödinger equation.

DERIVING THE EQUATION OF STATE FOR LIQUIDS AND EXTENSION OF THE PRINCIPLE OF CORRESPONDING STATES

A new simple model is introduced for a liquid and an equation of state is derived based on this model and the statistical mechanical calculations. This equation of state works well for the non-polar and slightly polar liquids. The important conclusion that may be deduced from this equation of state is that if the reduced variables of state are chosen and defined appropriately, then, the pri...

Modern Density Functional Theory (DFT), in principle, provides exact solution of time-independent Schrödinger equation, thus y

Prediction of Temperature Profile of a Buried Gas Pipeline Through Utilization of Corresponding States Principle

A new analytical equation for prediction of temperature profile of a buried gas pipeline is developed. Utility of this equation is illustrated by its application to corresponding states principle. The resulting equation is tested through prediction of the actual Schorre data. It is shown that the new equation can predict temperature profile more accurately than the others without using any char...