Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 112
... satisfy the condition af дх x = 0 = 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 дf = C1f ( 0 , t ) and = C2f ( L , t ) x = 0 дх x ...
... satisfy the condition af дх x = 0 = 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 дf = C1f ( 0 , t ) and = C2f ( L , t ) x = 0 дх x ...
Página 119
... satisfy ( 9.28 ) , one has L 72 д a x = L дха g dx - дх2 g g дх дх 1x = 0 = ( ß — ß ) ƒ ( L ) g ( L ) — ( a — ã ) ƒ ( 0 ) g ( 0 ) Hence , if a = a and ẞ = ẞ , the Laplacian d2 / dx2 is self - adjoint with the boundary conditions ( 9.28 ) ...
... satisfy ( 9.28 ) , one has L 72 д a x = L дха g dx - дх2 g g дх дх 1x = 0 = ( ß — ß ) ƒ ( L ) g ( L ) — ( a — ã ) ƒ ( 0 ) g ( 0 ) Hence , if a = a and ẞ = ẞ , the Laplacian d2 / dx2 is self - adjoint with the boundary conditions ( 9.28 ) ...
Página 186
... satisfy r2 dr dr 1.2 + k2 ] fi ( r ) = u ( r ) f ( r ) ( 13.45 ) [ ( 1 + dpd " + 1 ) 1.2 and the normalized spherical harmonics Y " satisfy LY , ( 0,9 ) = ( 1 + 1 ) Y , TM ( 0,9 ) ( 13.46 ) Since the Y , ( 0,9 ) form a complete set of ...
... satisfy r2 dr dr 1.2 + k2 ] fi ( r ) = u ( r ) f ( r ) ( 13.45 ) [ ( 1 + dpd " + 1 ) 1.2 and the normalized spherical harmonics Y " satisfy LY , ( 0,9 ) = ( 1 + 1 ) Y , TM ( 0,9 ) ( 13.46 ) Since the Y , ( 0,9 ) form a complete set of ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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