Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
Dentro del libro
Resultados 1-3 de 31
Página 81
... Suppose a sequence of polynomials P ( x ) is defined by xPn = αnPn + 1 + BnPn + YnPn - 1 Show that the eigenvalues of the matrix n = 0 , 1 , 2 , ... Po = 1 P - 1 = 0 Во хо 0 0 0 ... 0 0 0 κι βι αι 0 0 0 0 0 0 V2 βα α2 0 ... 0 0 0 M ...
... Suppose a sequence of polynomials P ( x ) is defined by xPn = αnPn + 1 + BnPn + YnPn - 1 Show that the eigenvalues of the matrix n = 0 , 1 , 2 , ... Po = 1 P - 1 = 0 Во хо 0 0 0 ... 0 0 0 κι βι αι 0 0 0 0 0 0 V2 βα α2 0 ... 0 0 0 M ...
Página 105
... suppose f1 ( x ) , ƒ2 ( x ) , ... , f ( x ) all satisfy Lfi = λfi for the same eigenvalue 2. Furthermore , suppose the f , are independent so that Σ a ; fï ( x ) = 0 i = 1 ( 8.27 ) implies a1 = 0 for all i . An orthogonal set is easily ...
... suppose f1 ( x ) , ƒ2 ( x ) , ... , f ( x ) all satisfy Lfi = λfi for the same eigenvalue 2. Furthermore , suppose the f , are independent so that Σ a ; fï ( x ) = 0 i = 1 ( 8.27 ) implies a1 = 0 for all i . An orthogonal set is easily ...
Página 248
... suppose that x + , is another solution Σm ,, ( x , + , ) = y ; i Then the § , must satisfy Σηξ === 0 Suppose at least one of the § , is not zero ( say §1 ) . One may write , by use of property IV and by repeated use of property VII ...
... suppose that x + , is another solution Σm ,, ( x , + , ) = y ; i Then the § , must satisfy Σηξ === 0 Suppose at least one of the § , is not zero ( say §1 ) . One may write , by use of property IV and by repeated use of property VII ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
Otras 19 secciones no mostradas
Otras ediciones - Ver todas
Términos y frases comunes
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