Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 11
... matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right . The product is then defined by ( mp ) is = Σ mikPkj k ( mx ) ; = Σm¡¡xj ( 1.29 ) As the reader will ...
... matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right . The product is then defined by ( mp ) is = Σ mikPkj k ( mx ) ; = Σm¡¡xj ( 1.29 ) As the reader will ...
Página 20
... matrix A commutes with another matrix B , then A commutes with any matrix of the form F ( B ) = Σ c „ B " where n is a positive integer and the c , are numbers . 12. Show that if A is any square matrix and I is the unit matrix , then IA ...
... matrix A commutes with another matrix B , then A commutes with any matrix of the form F ( B ) = Σ c „ B " where n is a positive integer and the c , are numbers . 12. Show that if A is any square matrix and I is the unit matrix , then IA ...
Página 64
... matrix . Any matrix H which satisfies the condition H H + is called a Hermitian matrix . Clearly , Hermitian matrices are normal matrices . Furthermore , any real symmetric matrix is a normal matrix , since such a matrix can be ...
... matrix . Any matrix H which satisfies the condition H H + is called a Hermitian matrix . Clearly , Hermitian matrices are normal matrices . Furthermore , any real symmetric matrix is a normal matrix , since such a matrix can be ...
Contenido
34 | 12 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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