Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página viii
... Representation of an Operator Motivation 6.2 The RC Line 6.3 Diagonalizing M 6.4 The Loaded String 6.5 Difference ... Representation of Linear Operators by Matrices 4.6 The Operator in the Dual Space 4.7 Effect of Change of Basis on the ...
... Representation of an Operator Motivation 6.2 The RC Line 6.3 Diagonalizing M 6.4 The Loaded String 6.5 Difference ... Representation of Linear Operators by Matrices 4.6 The Operator in the Dual Space 4.7 Effect of Change of Basis on the ...
Página 60
... representation in the u , basis of the identity operator , defined by the relation x = x for any vector x , is the unit matrix , since I = Σu , & ,, u ; = { uu * 1 , j ( 4.28 ) in agreement with the expansion theorem ( 4.9 ) . Clearly ...
... representation in the u , basis of the identity operator , defined by the relation x = x for any vector x , is the unit matrix , since I = Σu , & ,, u ; = { uu * 1 , j ( 4.28 ) in agreement with the expansion theorem ( 4.9 ) . Clearly ...
Página 70
... Representation of an Operator In the old notation the representation of a linear operator L in the basis / whose base vectors are the eigenvectors of L is given by L = & u , lut ( 4.31 ) The corresponding Dirac expression is L = | 1 > 1 ...
... Representation of an Operator In the old notation the representation of a linear operator L in the basis / whose base vectors are the eigenvectors of L is given by L = & u , lut ( 4.31 ) The corresponding Dirac expression is L = | 1 > 1 ...
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