Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 18
... 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 these columns which vanishes ; that is , the k n - columns m , are linearly independent if ...
... 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 these columns which vanishes ; that is , the k n - columns m , are linearly independent if ...
Página 133
... introduce the operator L = i a до - - x a ду 0 y ax ( 10.22 ) which also commutes with the Laplacian . Equations ( 10.19 ) , ( 10.20 ) , and ( 10.21 ) may then be written a + = eie ero ( 32 - 4 ) ә- = i0 V2 - 1 ( 10.19a ) ( + ) ( 10.20a ) ...
... introduce the operator L = i a до - - x a ду 0 y ax ( 10.22 ) which also commutes with the Laplacian . Equations ( 10.19 ) , ( 10.20 ) , and ( 10.21 ) may then be written a + = eie ero ( 32 - 4 ) ә- = i0 V2 - 1 ( 10.19a ) ( + ) ( 10.20a ) ...
Página 243
... introduce the 411 412 D ( A ) = | A | = a21 22 with the understanding that this is an abbreviation and that the value of A is obtained by evaluating the sum where € 12 = 1 , E21 = | A | = && , 911925 −1 , and ε11 = ε22 = 0. | A | = | a ...
... introduce the 411 412 D ( A ) = | A | = a21 22 with the understanding that this is an abbreviation and that the value of A is obtained by evaluating the sum where € 12 = 1 , E21 = | A | = && , 911925 −1 , and ε11 = ε22 = 0. | A | = | a ...
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