Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 10
... obtained by the following processes : Σ73 = Σ 22 : - ( Σm1xs ) ( max ) = ΣΣ Σ mij mikXjxk i , j , k It is to be noted that z , was written once with j as the summation index and once with k as the summation index in order to obtain the ...
... obtained by the following processes : Σ73 = Σ 22 : - ( Σm1xs ) ( max ) = ΣΣ Σ mij mikXjxk i , j , k It is to be noted that z , was written once with j as the summation index and once with k as the summation index in order to obtain the ...
Página 213
... obtained . Unfortunately , these lower bounds are not as useful in many applications as the upper bound already obtained . The first lower bound may be obtained as follows : Let and δ 2 = = f * Hf f + f ( Hf ) * ( Hf ) f + f ( 15.5 ) ...
... obtained . Unfortunately , these lower bounds are not as useful in many applications as the upper bound already obtained . The first lower bound may be obtained as follows : Let and δ 2 = = f * Hf f + f ( Hf ) * ( Hf ) f + f ( 15.5 ) ...
Página 223
... obtained by taking additional functions , and not by correcting previous ones . Unfortunately , as more functions y ... obtained with that obtained in Exercise 1 of Chap . 14 . 2. Find a lower bound for the eigenvalue of Exercise ...
... obtained by taking additional functions , and not by correcting previous ones . Unfortunately , as more functions y ... obtained with that obtained in Exercise 1 of Chap . 14 . 2. Find a lower bound for the eigenvalue of Exercise ...
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