Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 9
... indicated by utilizing it for writing the set of Eqs . ( 1.16 ) in the abbreviated form n * = Σ Σ m1jx ; + F , ( t ) i = 1 , 2 , . . . , n ( 1.24 ) j = 1 n The full notation Σ , which indicates both the variable of summation i = 1 and ...
... indicated by utilizing it for writing the set of Eqs . ( 1.16 ) in the abbreviated form n * = Σ Σ m1jx ; + F , ( t ) i = 1 , 2 , . . . , n ( 1.24 ) j = 1 n The full notation Σ , which indicates both the variable of summation i = 1 and ...
Página 202
... indicated in Eq . ( 14.4 ) one obtains Lf ̧ + € Lh + € 0f ̧ + e20h = λ „ f 。 + € λ ̧h + € μf 。 + e3μh εμιο Then , using ( 14.3 ) and dividing both sides of the resultant equation by e , there results Lh + Of + 0h 2h + μf + euμh In ...
... indicated in Eq . ( 14.4 ) one obtains Lf ̧ + € Lh + € 0f ̧ + e20h = λ „ f 。 + € λ ̧h + € μf 。 + e3μh εμιο Then , using ( 14.3 ) and dividing both sides of the resultant equation by e , there results Lh + Of + 0h 2h + μf + euμh In ...
Página 227
... indicating that it is a better approxi- mation to the eigencolumn . Continuing in this manner , one obtains Hence Ly2 ... indicated below . The rate of convergence of the method clearly depends upon the magnitude of the ratio Am - 1 / 2m ...
... indicating that it is a better approxi- mation to the eigencolumn . Continuing in this manner , one obtains Hence Ly2 ... indicated below . The rate of convergence of the method clearly depends upon the magnitude of the ratio Am - 1 / 2m ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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Términos y frases comunes
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