Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página v
... reader is introduced to approximation methods ( perturbation theory , variational methods , and numerical methods ) needed in treating most of the probleins of nature which confront the applied physicist . Certain background and ...
... reader is introduced to approximation methods ( perturbation theory , variational methods , and numerical methods ) needed in treating most of the probleins of nature which confront the applied physicist . Certain background and ...
Página 21
... reader will readily verify , dru dtn = Anu ( 2.2 ) whence , using the Taylor series expansion for u ( t ) about t = 0 , one obtains or t du 12 d2u u ( t ) = u ( 0 ) + + 1 ! dt 2 ! dt2 t = 0 = 1 + 1 ! 2 ! 1 At + A212 + u ( t ) = e1tu ( 0 ) ...
... reader will readily verify , dru dtn = Anu ( 2.2 ) whence , using the Taylor series expansion for u ( t ) about t = 0 , one obtains or t du 12 d2u u ( t ) = u ( 0 ) + + 1 ! dt 2 ! dt2 t = 0 = 1 + 1 ! 2 ! 1 At + A212 + u ( t ) = e1tu ( 0 ) ...
Página 276
... reader . Let < r , 0 > = f ( r , 0 ) and < k , n > = g ( k ) . Then the relations ( 2B.7 ) and ( 2B.8 ) yield the transforms 1 f ( r , 0 ) = = √ / 27 - 12 „ Z √ + ∞o 00 gn ( k ) eino J „ ( kr ) k dk ( 2B.45 ) 2π n = ∞ 0 and 1 gn ( k ) ...
... reader . Let < r , 0 > = f ( r , 0 ) and < k , n > = g ( k ) . Then the relations ( 2B.7 ) and ( 2B.8 ) yield the transforms 1 f ( r , 0 ) = = √ / 27 - 12 „ Z √ + ∞o 00 gn ( k ) eino J „ ( kr ) k dk ( 2B.45 ) 2π n = ∞ 0 and 1 gn ( k ) ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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Términos y frases comunes
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