Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página viii
... Operator Motivation 6.2 The RC Line 6.3 Diagonalizing M 6.4 The Loaded String 6.5 Difference Operators 3.5 The ... Operator in the Dual Space 4.7 Effect of Change of Basis on the Representation of an Operator 4.8 The Spectral ...
... Operator Motivation 6.2 The RC Line 6.3 Diagonalizing M 6.4 The Loaded String 6.5 Difference Operators 3.5 The ... Operator in the Dual Space 4.7 Effect of Change of Basis on the Representation of an Operator 4.8 The Spectral ...
Página 60
... operator is represented by a matrix L , then in the v , basis it is represented by sLs + , where s is the matrix which effects the transformation from the v , basis to the u , basis . Similarly , if + = L ; , u , * , then 1.j L = k , m ...
... operator is represented by a matrix L , then in the v , basis it is represented by sLs + , where s is the matrix which effects the transformation from the v , basis to the u , basis . Similarly , if + = L ; , u , * , then 1.j L = k , m ...
Página 61
... Operator In the preceding section it was supposed that the eigenvectors of the linear operator L formed a bi - orthonormal basis . This is not true for all operators . However , it is true for operators which satisfy the condition LL + ...
... Operator In the preceding section it was supposed that the eigenvectors of the linear operator L formed a bi - orthonormal basis . This is not true for all operators . However , it is true for operators which satisfy the condition LL + ...
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