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 1 = 1 n m1jx , + F , ( 1 ) i = 1 , 2 , . . . , n ( 1.24 ) The full notation Σ , which indicates both the variable of summation ime 1 and its ...
... indicated by utilizing it for writing the set of Eqs . ( 1.16 ) in the abbreviated form = n Σ 1 = 1 n m1jx , + F , ( 1 ) i = 1 , 2 , . . . , n ( 1.24 ) The full notation Σ , which indicates both the variable of summation ime 1 and its ...
Página 38
... indicated in Sec . 3.3 for some special cases . 3.2 The Cauchy - integral Formula The Cauchy - integral formula states that , if f ( Z ) has no singularities within or on the contour of integration C and if the point a lies within C ...
... indicated in Sec . 3.3 for some special cases . 3.2 The Cauchy - integral Formula The Cauchy - integral formula states that , if f ( Z ) has no singularities within or on the contour of integration C and if the point a lies within C ...
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
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх