Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 275
... Fourier cosine transform of the function f ( x ) . The Fourier sine and cosine series expansions ( 2B.37 ) and ( 2B.40 ) are equivalent in the range 0 ≤ x ≤ L. They differ in that if it is desired to expand a function between -L and + ...
... Fourier cosine transform of the function f ( x ) . The Fourier sine and cosine series expansions ( 2B.37 ) and ( 2B.40 ) are equivalent in the range 0 ≤ x ≤ L. They differ in that if it is desired to expand a function between -L and + ...
Página 276
... Fourier - Bessel or Hankel Transforms . Substitution of ( 2B.50 ) into ( 2B.49 ) yields the Fourier - Bessel integral ƒ ( r ) = [ ® [ ƒ ^ ƒ ( r ' ) J „ ( kr ° ) r ° dr ' ] J „ ( kr ) k dk ( 2B.51 ) f which is the analogue of the cosine ...
... Fourier - Bessel or Hankel Transforms . Substitution of ( 2B.50 ) into ( 2B.49 ) yields the Fourier - Bessel integral ƒ ( r ) = [ ® [ ƒ ^ ƒ ( r ' ) J „ ( kr ° ) r ° dr ' ] J „ ( kr ) k dk ( 2B.51 ) f which is the analogue of the cosine ...
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
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх