Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 53
... space . Any vector x may be written as2 X = , щ ; x ; ( 4.6 ) i = 1 The set of vectors u , is said to form a basis . The x , are the components of the vector x in this basis . For convenience , this ... VECTOR SPACES AND LINEAR OPERATORS 53.
... space . Any vector x may be written as2 X = , щ ; x ; ( 4.6 ) i = 1 The set of vectors u , is said to form a basis . The x , are the components of the vector x in this basis . For convenience , this ... VECTOR SPACES AND LINEAR OPERATORS 53.
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 = Lx ( 4.15 ) Lis a known operator if and only if , given x , y is determined . The linearity ...
... 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 = Lx ( 4.15 ) Lis a known operator if and only if , given x , y is determined . The linearity ...
Página 266
... vector spaces . The Dirac notation introduced in Chap . 5 will be used as well as the standard notion found in ... space and let the set of kets | 2 > form a basis in this space . Since the space is of dimensionality N , there will be N ...
... vector spaces . The Dirac notation introduced in Chap . 5 will be used as well as the standard notion found in ... space and let the set of kets | 2 > form a basis in this space . Since the space is of dimensionality N , there will be N ...
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