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
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
Derechos de autor | |
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Términos y frases comunes
analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх