Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 283
... path of integration W , is equal 1 to W1 + W2 . 4π 3π π π 2π 3π 4π ધૃ Figure 2C.1 . Allowed regions in the w plane . Expression ( 2C.10 ) for the integral representation of the cylindrical functions Z , may now be written Z , ( p ) ...
... path of integration W , is equal 1 to W1 + W2 . 4π 3π π π 2π 3π 4π ધૃ Figure 2C.1 . Allowed regions in the w plane . Expression ( 2C.10 ) for the integral representation of the cylindrical functions Z , may now be written Z , ( p ) ...
Página 288
... path of integration does not pass through a singularity of the integrand . Let z = x + iy_and_f ( z ) = u ( x , y ) ... path as possible we must avoid the mountains and keep to the valleys as much as possible . In the interesting case ...
... path of integration does not pass through a singularity of the integrand . Let z = x + iy_and_f ( z ) = u ( x , y ) ... path as possible we must avoid the mountains and keep to the valleys as much as possible . In the interesting case ...
Página 289
... path . Such a path is called a line of steepest ascent and descent . There will be one into each valley . If zo is a saddle point , f ( z ) near it can be expanded in the form f ( z ) = ƒ ( zo ) + 1⁄2 ( z − zo ) 2ƒ ̋ ( zo ) + and the ...
... path . Such a path is called a line of steepest ascent and descent . There will be one into each valley . If zo is a saddle point , f ( z ) near it can be expanded in the form f ( z ) = ƒ ( zo ) + 1⁄2 ( z − zo ) 2ƒ ̋ ( zo ) + and the ...
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