Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 27
... eigen- values is the subject of the next section . 2.5 Diagonalization of Nondegenerate Matrices In the past few sections it has been indicated that a knowledge of the eigenvalues and eigencolumns of a matrix A enables the evaluation of ...
... eigen- values is the subject of the next section . 2.5 Diagonalization of Nondegenerate Matrices In the past few sections it has been indicated that a knowledge of the eigenvalues and eigencolumns of a matrix A enables the evaluation of ...
Página 207
... eigen- value # 2 may be found as follows : From ( 14.23 ) one has y " + ( dy ) " = − ( λ + dâ ) ( ƒ + dƒ ) ( y + dy ) or ( dy ) " + îƒ dy = − y ( ƒ då + å dƒ ) Hence , with z = dy , πx ( dλ π2 z " + 2zsin #x ( 8λ + # 2 df ) A solution ...
... eigen- value # 2 may be found as follows : From ( 14.23 ) one has y " + ( dy ) " = − ( λ + dâ ) ( ƒ + dƒ ) ( y + dy ) or ( dy ) " + îƒ dy = − y ( ƒ då + å dƒ ) Hence , with z = dy , πx ( dλ π2 z " + 2zsin #x ( 8λ + # 2 df ) A solution ...
Página 227
... eigen- column are determined , whereas in many problems it is the lowest eigen- value and its eigencolumn which are of interest ; the method cannot be applied to continuous systems involving differential operators . Some methods for ...
... eigen- column are determined , whereas in many problems it is the lowest eigen- value and its eigencolumn which are of interest ; the method cannot be applied to continuous systems involving differential operators . Some methods for ...
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