Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 142
... Bessel functions must satisfy the boundary condition Jn ( kp ) = 0. This condition determines the eigenvalues as follows : The Bessel function J ( 2 ) is zero only for certain values of 2 , say 21 , λn2 , .... From the properties of ...
... Bessel functions must satisfy the boundary condition Jn ( kp ) = 0. This condition determines the eigenvalues as follows : The Bessel function J ( 2 ) is zero only for certain values of 2 , say 21 , λn2 , .... From the properties of ...
Página 276
... 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 integral ( 2B.51 ) ...
... 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 integral ( 2B.51 ) ...
Página 296
... Bessel functions ) Debye , P. , 291 , 292 Degenerate matrix , 26 Delta , Kronecker , 12 Delta function , 98-100 Determinant , 14-15 , 243-251 of matrix product , 15 , 250-251 Diagonal matrix , 7 Diagonalization of matrix , 26-27 , 64 ...
... Bessel functions ) Debye , P. , 291 , 292 Degenerate matrix , 26 Delta , Kronecker , 12 Delta function , 98-100 Determinant , 14-15 , 243-251 of matrix product , 15 , 250-251 Diagonal matrix , 7 Diagonalization of matrix , 26-27 , 64 ...
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