Application of the Lagrange Multiplier Method the Semi-Inverse Method to the Search for Generalized Variational Principle in Quantum Mechanics

2003 ◽  
Vol 4 (3) ◽  
Author(s):  
Tian-Hu Hao
Keyword(s):  
Quantum Mechanics ◽  
Variational Principle ◽  
Lagrange Multiplier ◽  
Inverse Method ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Generalized Variational Principle

Lagrange crisis and generalized variational principle for 3D unsteady flow

2019 ◽  
Vol 30 (3) ◽  
pp. 1189-1196 ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Variational Principle ◽  
Unsteady Flow ◽  
Lagrange Multiplier ◽  
Unknown Function ◽  
Inverse Method ◽  
Variational Principles ◽  
Multiplier Method ◽  
Generalized Variational Principle ◽  
Content Type ◽  
3D Unsteady Flow

Purpose A three-dimensional (3D) unsteady potential flow might admit a variational principle. The purpose of this paper is to adopt a semi-inverse method to search for the variational formulation from the governing equations. Design/methodology/approach A suitable trial functional with a possible unknown function is constructed, and the identification of the unknown function is given in detail. The Lagrange multiplier method is used to establish a generalized variational principle, but in vain. Findings Some new variational principles are obtained, and the semi-inverse method can easily overcome the Lagrange crisis. Practical implications The semi-inverse method sheds a promising light on variational theory, and it can replace the Lagrange multiplier method for the establishment of a generalized variational principle. It can be used for the establishment of a variational principle for fractal and fractional calculus. Originality/value This paper establishes some new variational principles for the 3D unsteady flow and suggests an effective method to eliminate the Lagrange crisis.

scholarly journals On the semi-inverse method and variational principle

2013 ◽  
Vol 17 (5) ◽  
pp. 1565-1568 ◽  
Author(s):  
Xue-Wei Li ◽  
Ya Li ◽  
Ji-Huan He
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Inverse Method ◽  
Generalized Variational Principle ◽  
Open Forum ◽  
One Dimensional ◽  
History Of

In this Open Forum, Liu et al. proved the equivalence between He-Lee 2009 variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., Thermal Science, 17(2013), pp. 951-952) for one dimensional heat conduction. We confirm the correction of Liu et al.?s proof, and give a short remark on the history of the semi-inverse method for establishment of a generalized variational principle.

scholarly journals Lagrange Multiplier Method for Drilling Oil Reservoir

2017 ◽  
Vol 06 (03) ◽  
Author(s):  
Vasant P ◽  
Maung MT ◽  
Min YW ◽  
Tun HM ◽  
Thant KZ
Keyword(s):  
Lagrange Multiplier ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Oil Reservoir
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