Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 12
... ( column ) x . The result is a 1 × 1 matrix zx given by n ZX = Στίχ i = 1 ( 1.37 ) In words the prescription becomes : To multiply the row z into the column x , multiply the leftmost element of z by the topmost element of x ; then ...
... ( column ) x . The result is a 1 × 1 matrix zx given by n ZX = Στίχ i = 1 ( 1.37 ) In words the prescription becomes : To multiply the row z into the column x , multiply the leftmost element of z by the topmost element of x ; then ...
Página 25
... column u as a linear combination of the eigenvectors of A suffices to enable the evaluation of f ( A ) and the solution of the initial value problems earlier considered . It will now be shown that an arbitrary column u may be written as ...
... column u as a linear combination of the eigenvectors of A suffices to enable the evaluation of f ( A ) and the solution of the initial value problems earlier considered . It will now be shown that an arbitrary column u may be written as ...
Página 248
... column y for the kth column of IM . The reader will note the equivalence of this with the solution previously given for two equations in two unknowns . To demonstrate the uniqueness of the solution , we suppose that x + , is another ...
... column y for the kth column of IM . The reader will note the equivalence of this with the solution previously given for two equations in two unknowns . To demonstrate the uniqueness of the solution , we suppose that x + , is another ...
Contenido
34 | 12 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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Términos y frases comunes
approximate arbitrary asymptotic ax² base vectors basis Bessel functions boundary conditions Chap coefficients consider constant continuous systems contour corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation eigen eigencolumns eigenfunctions eigenvalue problem eigenvectors elements evaluate expansion finite number follows formula given Green's function Hence Hermitian matrix Hermitian operator infinite integral representation integral theorem inverse Laplace transform linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company method multiplication nonsingular normal matrix obtained orthonormality conditions perturbation procedure relations result Ritz method satisfies scattering sinh solution solve spherical substitution transformation functions trial functions vanish variable vector space Verify wave whence write written x₁ y₁ yields York zero ηπχ παχ ди ду дх