Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página viii
... Linear Operators 4.1 Introduction · 4.2 Base Vectors and Basis 43 44 46 47 50 50 52 4.3 Change of Basis 4.4 Linear Operators 4.5 The Representation of Linear Operators by Matrices 4.6 The Operator in the Dual Space 55 57 57 58 ...
... Linear Operators 4.1 Introduction · 4.2 Base Vectors and Basis 43 44 46 47 50 50 52 4.3 Change of Basis 4.4 Linear Operators 4.5 The Representation of Linear Operators by Matrices 4.6 The Operator in the Dual Space 55 57 57 58 ...
Página 57
... Linear Operators An operator L , in a vector space , is an entity which , acting upon an arbitrary vector x , converts it into a vector y : y ... OPERATORS 57 The Representation of Linear Operators by Matrices The Operator in the Dual Space.
... Linear Operators An operator L , in a vector space , is an entity which , acting upon an arbitrary vector x , converts it into a vector y : y ... OPERATORS 57 The Representation of Linear Operators by Matrices The Operator in the Dual Space.
Página 61
... Linear 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 ...
... Linear 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 ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх