Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 144
... normalized solutions of ( 10.3 ) which are bounded as x2 + y2 approaches infinity are 1 fo ( x , y ) = ei ( wxx + wy ¥ ) 2π 2. Carry out the indicated operations over w , and ∞ , in ( 10.7 ) and thus obtain ( 10.8 ) . 3. Verify that ...
... normalized solutions of ( 10.3 ) which are bounded as x2 + y2 approaches infinity are 1 fo ( x , y ) = ei ( wxx + wy ¥ ) 2π 2. Carry out the indicated operations over w , and ∞ , in ( 10.7 ) and thus obtain ( 10.8 ) . 3. Verify that ...
Página 153
... normalization of the eigen- function . It has the value1 C1 = ( -1 ) ' √ ( 2 + 1 ) ! 1 4πT 21 ! We denote the normalized eigenfunction by Y , ' ( 0 , v ) ¥ 1,1 ( 0 , q ) = Y¿1 ( 0 , q ) = ( −1 ) 2 ( 11.35 ) ( 21 + 1 ) ! 1 ( x + 4πT 12 ...
... normalization of the eigen- function . It has the value1 C1 = ( -1 ) ' √ ( 2 + 1 ) ! 1 4πT 21 ! We denote the normalized eigenfunction by Y , ' ( 0 , v ) ¥ 1,1 ( 0 , q ) = Y¿1 ( 0 , q ) = ( −1 ) 2 ( 11.35 ) ( 21 + 1 ) ! 1 ( x + 4πT 12 ...
Página 154
Gerald Goertzel, Nunzio Tralli. The definition of the normalized spherical harmonics given here corresponds to that of Condon and Shortley.1 It ... normalized spherical harmonics 154 SYSTEMS WITH AN INFINITE NUMBER OF DEGREES OF FREEDOM.
Gerald Goertzel, Nunzio Tralli. The definition of the normalized spherical harmonics given here corresponds to that of Condon and Shortley.1 It ... normalized spherical harmonics 154 SYSTEMS WITH AN INFINITE NUMBER OF DEGREES OF FREEDOM.
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