Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página viii
... Operator 4.8 The Spectral Representation of an Operator 4.9 The Formation of a Basis by Eigenvectors of a Linear Operator 4.10 The Diagonalization of Normal Matrices Chapter 5 The Dirac Notation 5.1 59 60 61 64 67 67 5.2 The Change of ...
... Operator 4.8 The Spectral Representation of an Operator 4.9 The Formation of a Basis by Eigenvectors of a Linear Operator 4.10 The Diagonalization of Normal Matrices Chapter 5 The Dirac Notation 5.1 59 60 61 64 67 67 5.2 The Change of ...
Página 57
... 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 = Lx ( 4.15 ) L is a known operator if and only if , given x , y is determined . The linearity of the ...
... 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 = Lx ( 4.15 ) L is a known operator if and only if , given x , y is determined . The linearity of the ...
Página 60
... operator L 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 + = ΣuLu * , then i , j L + = Σ ...
... operator L 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 + = ΣuLu * , then i , j L + = Σ ...
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