Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 112
... satisfy the condition af дх = Cf ( 0 , t ) where C is a constant . 3. The finite domain , 0 ≤ x ≤ L The boundary conditions on the functions f ( x , t ) in this domain are af дх af = C1f ( 0,1 ) and = C2f ( L , t ) дх x = L x = 0 ...
... satisfy the condition af дх = Cf ( 0 , t ) where C is a constant . 3. The finite domain , 0 ≤ x ≤ L The boundary conditions on the functions f ( x , t ) in this domain are af дх af = C1f ( 0,1 ) and = C2f ( L , t ) дх x = L x = 0 ...
Página 119
... satisfy ( 9.28 ) , one has a Ꮮ [ ( 1 2 8 - 8 3 1 ) dx - ( 1/2 8 -8 ) 08 = g ax = g g ax a ax = ( ß — ß ) ƒ ( L ) g ( L ) — ( a — ā ) ƒ ( 0 ) g ( 0 ) - Hence , if a α and ẞ B , the Laplacian d2 / dx2 is self - adjoint with the boundary ...
... satisfy ( 9.28 ) , one has a Ꮮ [ ( 1 2 8 - 8 3 1 ) dx - ( 1/2 8 -8 ) 08 = g ax = g g ax a ax = ( ß — ß ) ƒ ( L ) g ( L ) — ( a — ā ) ƒ ( 0 ) g ( 0 ) - Hence , if a α and ẞ B , the Laplacian d2 / dx2 is self - adjoint with the boundary ...
Página 186
... satisfy [ d d I ( 1 + 1 ) + k2 ] fi ( r ) = u ( r ) f ( r ) ( 13.45 ) 12 dr dr and the normalized spherical harmonics Y TM satisfy Ľ2Y , TM ( 0 , q ) = 1 ( 1 + 1 ) Y , TM ( 0,9 ) ( 13.46 ) Since the Y , ( 0,9 ) form a complete set of ...
... satisfy [ d d I ( 1 + 1 ) + k2 ] fi ( r ) = u ( r ) f ( r ) ( 13.45 ) 12 dr dr and the normalized spherical harmonics Y TM satisfy Ľ2Y , TM ( 0 , q ) = 1 ( 1 + 1 ) Y , TM ( 0,9 ) ( 13.46 ) Since the Y , ( 0,9 ) form a complete set of ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх