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 225
... eigen- column ym . If the operator has a complete set of eigencolumns . ( σ = 1 , 2 , ... , m ) such that σ Уфо = Рофо ( 16.2 ) 1221 ≤ 1221 < . · · ≤ 12 ml ( 16.3 ) Yo = Σa.b. Σασφα ( 16.4 ) one may write , for arbitrary yo , σ Then ...
... eigen- column ym . If the operator has a complete set of eigencolumns . ( σ = 1 , 2 , ... , m ) such that σ Уфо = Рофо ( 16.2 ) 1221 ≤ 1221 < . · · ≤ 12 ml ( 16.3 ) Yo = Σa.b. Σασφα ( 16.4 ) one may write , for arbitrary yo , σ Then ...
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
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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