Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 4
... replaced by the pair of equations below which contain only first time derivatives : mx = y y = -kx ( 1.5 ) Similarly , second time derivatives may be eliminated from Eqs . ( 1.4 ) by the introduction of the two new dependent variables ...
... replaced by the pair of equations below which contain only first time derivatives : mx = y y = -kx ( 1.5 ) Similarly , second time derivatives may be eliminated from Eqs . ( 1.4 ) by the introduction of the two new dependent variables ...
Página 191
... replaced by since d - dr d ( 1 + 1 ) + + k2 £ 1,00 = u ( r ) fi ( 13.66 ) 1 ) . [ 1 d d _ " + 1 ) + 1 ] Si , inc = 0 dr dr Then , replacing f , in the right - hand member of ( 13.66 ) by finc and using the auxiliary Green's function g1 ...
... replaced by since d - dr d ( 1 + 1 ) + + k2 £ 1,00 = u ( r ) fi ( 13.66 ) 1 ) . [ 1 d d _ " + 1 ) + 1 ] Si , inc = 0 dr dr Then , replacing f , in the right - hand member of ( 13.66 ) by finc and using the auxiliary Green's function g1 ...
Página 228
... replaced by the problem L ̄1y = λ ̃1y ( 16.8 ) Clearly , the largest eigenvalue of -1 to which the iteration method con- verges yields the lowest eigenvalue of £ . Unfortunately , the labor of inverting in the case of discrete systems ...
... replaced by the problem L ̄1y = λ ̃1y ( 16.8 ) Clearly , the largest eigenvalue of -1 to which the iteration method con- verges yields the lowest eigenvalue of £ . Unfortunately , the labor of inverting in the case of discrete systems ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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Términos y frases comunes
approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх