Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 23
... eigencolumns such that u ( 0 ) may be written as a linear combination ( superposition ) of these eigencolumns . In such a case , a solution almost as simple in form as that of ( 2.9 ) is obtained . Thus , let the eigencolumns of A be ...
... eigencolumns such that u ( 0 ) may be written as a linear combination ( superposition ) of these eigencolumns . In such a case , a solution almost as simple in form as that of ( 2.9 ) is obtained . Thus , let the eigencolumns of A be ...
Página 25
... eigencolumns of A if and only if A has n linearly independent eigencolumns . Thus , if A has less than ʼn linearly independ- ent eigencolumns , the resultant linear superposition will depend on less than n arbitrary constants , whereas ...
... eigencolumns of A if and only if A has n linearly independent eigencolumns . Thus , if A has less than ʼn linearly independ- ent eigencolumns , the resultant linear superposition will depend on less than n arbitrary constants , whereas ...
Página 28
... eigencolumns are linearly dependent and it will be shown that this assumption leads to a contradiction . If the eigencolumns are linearly dependent , there exists a set of numbers a1 , not all zero , such that Σs.iai = 0 ( 2.25 ) The ...
... eigencolumns are linearly dependent and it will be shown that this assumption leads to a contradiction . If the eigencolumns are linearly dependent , there exists a set of numbers a1 , not all zero , such that Σs.iai = 0 ( 2.25 ) The ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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Términos y frases comunes
approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх