Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 109
... differential operator of the form D ( r ) = αV2 + ß where a and ẞ are constants and V2 is the Laplacian operator ... equation l ( r , r ' ) = D ( r ) d ( r — r ′ ) reduces to the conventional - Lf ( r ) = g ( r ) ( ordinary or partial ) ...
... differential operator of the form D ( r ) = αV2 + ß where a and ẞ are constants and V2 is the Laplacian operator ... equation l ( r , r ' ) = D ( r ) d ( r — r ′ ) reduces to the conventional - Lf ( r ) = g ( r ) ( ordinary or partial ) ...
Página 141
... differential equation for the circular membrane is the same as for the rectangular one , but the boundary condition is different : the trans- verse displacement y is always zero on a circle of radius p about the origin . To solve the ...
... differential equation for the circular membrane is the same as for the rectangular one , but the boundary condition is different : the trans- verse displacement y is always zero on a circle of radius p about the origin . To solve the ...
Página 156
... Eq . ( 11.51 ) shows that satisfies the same differential equation as F - 1 . Since the differential equation determines F11 to within a multiplicative constant ( if F - 1 is regular at p = 0 ) , one has ( 2 + P d F1 = C1F1 - 1 ...
... Eq . ( 11.51 ) shows that satisfies the same differential equation as F - 1 . Since the differential equation determines F11 to within a multiplicative constant ( if F - 1 is regular at p = 0 ) , one has ( 2 + P d F1 = C1F1 - 1 ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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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