Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 276
... Fourier - Bessel or Hankel Transforms . Substitution of ( 2B.50 ) into ( 2B.49 ) yields the Fourier - Bessel integral f ( r ) [ ƒ “ ƒ ( r ' ) J „ ( kr ' ) r ' dr ' ] J „ ( kr ) k dk = 0 which is the analogue of the cosine Fourier ...
... Fourier - Bessel or Hankel Transforms . Substitution of ( 2B.50 ) into ( 2B.49 ) yields the Fourier - Bessel integral f ( r ) [ ƒ “ ƒ ( r ' ) J „ ( kr ' ) r ' dr ' ] J „ ( kr ) k dk = 0 which is the analogue of the cosine Fourier ...
Página 279
... Fourier - Bessel ex- pansion of a function of r and 0 . References Carslaw , H. S .: " Fourier's Series and Integrals , " The Macmillan Company , New York , 1930 . Wiener , N .: " The Fourier Integral , " Cambridge University Press ...
... Fourier - Bessel ex- pansion of a function of r and 0 . References Carslaw , H. S .: " Fourier's Series and Integrals , " The Macmillan Company , New York , 1930 . Wiener , N .: " The Fourier Integral , " Cambridge University Press ...
Página 296
... Fourier series , 275 Cosine Fourier transform , 269 , 275 Courant , R. , 175 , 210 , 224 , 260 Cramer's rule , 248 Cross section , differential scattering , 184 Cylindrical functions , 134 , 280-294 integral representation of , 280-286 ...
... Fourier series , 275 Cosine Fourier transform , 269 , 275 Courant , R. , 175 , 210 , 224 , 260 Cramer's rule , 248 Cross section , differential scattering , 184 Cylindrical functions , 134 , 280-294 integral representation of , 280-286 ...
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