Klein-Gordon equation in Schrödinger form

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Klein-Gordon equation in Schrödinger form

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some aspects appear here connected with as say orof dr mircea orasanu and prof horia orasanu as followings

ON GORDON EQUATION AND GRADIENTS

Authors Horia Orasanu and Mircea Orasanu

ABSTRACT

The integrand on the left side is F, i.e. the divergence of F. Also, notice that cos(n,i), cos(n,j), and cos(n,k) are the components of the normal unit vector n, so the integrand on the right side is simply Fn, i.e., the dot product of F and the unit normal to the surface. Hence we can express the Divergence Theorem in its familiar form

Several interesting facts can be deduced from this theorem. For example, if we define F as the gradient of the scalar field (x,y,z) we can substitute for F in the above formula to give

The integrand of the volume integral on the left is the Laplacian of , so if is harmonic (i.e., a solution of Laplace’s equation) the left side vanishes

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