Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 111
... boundary conditions af дх 0 af дх x = L = C1f ( 0,1 ) = C2f ( L , t ) In these equations f ( x , t ) represented the ... satisfies the boundary conditions that it remain finite as x approaches∞0 . 2. The semi - infinite domain , 0 < x ...
... boundary conditions af дх 0 af дх x = L = C1f ( 0,1 ) = C2f ( L , t ) In these equations f ( x , t ) represented the ... satisfies the boundary conditions that it remain finite as x approaches∞0 . 2. The semi - infinite domain , 0 < x ...
Página 143
... satisfies the boundary condition 0 < r < a n = 0 , 1 , 2 , ... ( 10.61 ) J2 ( ka ) = 0 ( 10.62 ) In the case of the circular ring the eigenfunctions are given by fx.n ( r , 0 ) = [ J ( kr ) + cN „ ( kr ) ] eino 0 < b < r < a n = 0 , ± 1 ...
... satisfies the boundary condition 0 < r < a n = 0 , 1 , 2 , ... ( 10.61 ) J2 ( ka ) = 0 ( 10.62 ) In the case of the circular ring the eigenfunctions are given by fx.n ( r , 0 ) = [ J ( kr ) + cN „ ( kr ) ] eino 0 < b < r < a n = 0 , ± 1 ...
Página 228
... satisfies the boundary conditions . Then , integrating twice and applying the boundary conditions one obtains = Yı -12x + 6x3- 12x4 = −12 ( x − 2x3 + x1 ) = -122 ′′ Continuing this process , one obtains the successive iterates : Y2 ...
... satisfies the boundary conditions . Then , integrating twice and applying the boundary conditions one obtains = Yı -12x + 6x3- 12x4 = −12 ( x − 2x3 + x1 ) = -122 ′′ Continuing this process , one obtains the successive iterates : Y2 ...
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