Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 18
... linear superposition of the columns of the matrix . To proceed further , it is useful to introduce the concept of linear inde- pendence . A set of n columns is said to be linearly independent if there exists no linear combination of ...
... linear superposition of the columns of the matrix . To proceed further , it is useful to introduce the concept of linear inde- pendence . A set of n columns is said to be linearly independent if there exists no linear combination of ...
Página 25
... linear combination of the eigencolumns of A if and only if A has n linearly independent eigencolumns . Thus , if A has less than n linearly independ- ent eigencolumns , the resultant linear superposition will depend on less than n ...
... linear combination of the eigencolumns of A if and only if A has n linearly independent eigencolumns . Thus , if A has less than n linearly independ- ent eigencolumns , the resultant linear superposition will depend on less than n ...
Página 53
... linearly independent vectors in the space , but any n + 1 vectors are linearly dependent . " That this is always possible if the u , are linearly independent may be demonstrated as follows : let u1 ,. u , be lincarly independent , and ...
... linearly independent vectors in the space , but any n + 1 vectors are linearly dependent . " That this is always possible if the u , are linearly independent may be demonstrated as follows : let u1 ,. u , be lincarly independent , and ...
Contenido
34 | 12 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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approximate arbitrary asymptotic ax² base vectors basis Bessel functions boundary conditions Chap coefficients consider constant continuous systems contour corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation eigen eigencolumns eigenfunctions eigenvalue problem eigenvectors elements evaluate expansion finite number follows formula given Green's function Hence Hermitian matrix Hermitian operator infinite integral representation integral theorem inverse Laplace transform linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company method multiplication nonsingular normal matrix obtained orthonormality conditions perturbation procedure relations result Ritz method satisfies scattering sinh solution solve spherical substitution transformation functions trial functions vanish variable vector space Verify wave whence write written x₁ y₁ yields York zero ηπχ παχ ди ду дх