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independent equation
The proof makes the same assumptions as the corresponding proof for the time independent equation.
      
A proof is repeated here which was given in earlier papers and which shows that, on the basis of a reasonable assumption, this definiton of probability density leads straight to Schr?dinger's time-independent equation.
      
Formally, it is obtainable from the previous time-independent equation by replacing the energy E with .
      
Exchange processes between the "external variables? of a system and its surroundings and hence also the influence of kinetic and potential energy are described by another independent equation, i.e.
      
Surface water storage independent equation for predicting furrow irrigation advance
      
Next, each independent equation is made analogous to the corresponding problem of a beam on an elastic foundation.
      
This treatment requires the development of results concerning the time-independent equation u + Σi = 1n (φi(u))xi = h for h∈L1(Rn), which in turn is studied via the regularized equation
      
However, our solution satisfies this independent equation.
      
The time-independent equation that describes this modulated wave is shown to be the stationary Schr?dinger equation (or the Klein-Gordon equation in the relativistic version).
      
The projection matrix-dyads defining all the 16 independent equation solutions are found.
      
A sixth independent equation can be obtained to permit a complete stress solution by using the double-exposure hologram technique in conjunction with an immersion tank.
      
It will be shown that Newton's law of impact for two colliding point masses can be derived from the concept of energy conservation and the principle of maximum dissipation, and has therefore not to be regarded as an independent equation.
      
An analog of the kernel of the time-independent equation is proposed, leading to solvability conditions on the inhomogeneous term.
      
To produce a universal, sample-independent equation, r must be eliminated.
      
Therefore, on each boundary, four independent equation sets are obtained.
      
The key new feature that is added to the shallow water dynamics here is an independent equation for conservation of water.
      
The time dependent equation is a first order linear evolution equation, whereas the time-independent equation is a linear eigenvalue equation.
      
 

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