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
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