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
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
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analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх