Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 11
... definition will be given here . The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right . The product is then defined by ( mp ) is = Σ ...
... definition will be given here . The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right . The product is then defined by ( mp ) is = Σ ...
Página 97
... the boundary conditions ( 8.4 ) is Hermitian . It is incorrect to omit the italic phrase . The boundary conditions are part of the definition of the operator . When an operator is defined by ( 8.6 ) , OPERATORS IN CONTINUOUS SYSTEMS 97.
... the boundary conditions ( 8.4 ) is Hermitian . It is incorrect to omit the italic phrase . The boundary conditions are part of the definition of the operator . When an operator is defined by ( 8.6 ) , OPERATORS IN CONTINUOUS SYSTEMS 97.
Página 98
... defined so that if g ( x ) Lf ( x ) , then d2 g ( x ) = f ( x ) dx2 ƒ ( 0 ) = f ( L ) = 0 ( 8.7 ) ( 8.8 ) These relations have an obvious similarity to ( 8.3 ) and ( 8.4 ) . That as defined in ( 8.7 ) and ( 8.8 ) cannot be readily put ...
... defined so that if g ( x ) Lf ( x ) , then d2 g ( x ) = f ( x ) dx2 ƒ ( 0 ) = f ( L ) = 0 ( 8.7 ) ( 8.8 ) These relations have an obvious similarity to ( 8.3 ) and ( 8.4 ) . That as defined in ( 8.7 ) and ( 8.8 ) cannot be readily put ...
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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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