variational method

variational method

[‚ver·ē′ā·shən·əl ‚meth·əd]
(quantum mechanics)
A method of calculating an upper bound on the lowest energy level of a quantum-mechanical system and an approximation for the corresponding wave function; in the integral representing the expectation value of the Hamiltonian operator, one substitutes a trial function for the true wave function, and varies parameters in the trial function to minimize the integral.
References in periodicals archive ?
In adaptive thresholding based on variational method, the first step is to divide the image into a regular grid of different sub regions which are adjoint and the second step is to assign different threshold to the centre of each sub region.
Feodosiev used successfully the Papkovich variational method for particular problems.
We envision that the 4D-Var and hybrid of variational method and EnKF hold great promise for the future improvement of NWP for the convective scale because of their abilities in obtaining initial conditions that contain convective-scale balances.
The modal methods such as the Mode Matching (MM) technique [1], the Generalized Scattering Matrix (GSM) analysis [2] and the Multimodal Variational Method (MVM) [3], use a modal development of electromagnetic fields on the basis of eigenmodes of constituent waveguides.
Over 250 papers explore such topics as forecast models and their comparison in tourism passengers in Gansu Province, a mobility performance analysis of an outdoor mobile robot with foldable wheels, a weighted moving average passive aggressive algorithm for online portfolio selection, mammographic mass segmentation using a variational method, the design and implementation of a tank agent in combat situations, the modeling and design of networked control systems based on reduced dimension observers, and analyzing and countering flight delay based on statistical data.
Analytical investigation of strongly nonlinear normal mode using HPM and He's variational method, Journal of Applied Functional Analysis 4(1): 682-691.
3 and 4 asymmetric, it is found that when the initial power is high and comparable to the critical power, there is a substantial discrepancy between the analytical predictions by the variational method and the numerical simulation results.
Vainberg, Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations, John Wiley, New York, 1973.
This paper is concerned with the variational method to solve the NLS equation.
Use of the direct variational method for the study of one- and two-electron atomic systems confined by spherical penetrable boxes.
1973, Dual variational method in critical point theory and applications, Journal of functional analysis, 14, pp.
6] Some design procedures have been reported based on a number of methods such as the variational method,[1] mode-matching method[2] and residue-calculus technique.

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