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 |
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