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 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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Términos y frases comunes
approximate arbitrary asymptotic ax² base vectors basis Bessel functions boundary conditions Chap coefficients consider constant continuous systems contour corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation eigen eigencolumns eigenfunctions eigenvalue problem eigenvectors elements evaluate expansion finite number follows formula given Green's function Hence Hermitian matrix Hermitian operator infinite integral representation integral theorem inverse Laplace transform linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company method multiplication nonsingular normal matrix obtained orthonormality conditions perturbation procedure relations result Ritz method satisfies scattering sinh solution solve spherical substitution transformation functions trial functions vanish variable vector space Verify wave whence write written x₁ y₁ yields York zero ηπχ παχ ди ду дх