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
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
Derechos de autor | |
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Términos y frases comunes
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