Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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... vector changes in a corresponding way . To each state of the physical system there corresponds a unique state vector and vice versa . The state vector is an abstract quantity which may be described mathe- matically in a number of ...
... vector changes in a corresponding way . To each state of the physical system there corresponds a unique state vector and vice versa . The state vector is an abstract quantity which may be described mathe- matically in a number of ...
Página 52
... vector spaces . As a starting point , recall that the position of a particle in a given cartesian coordinate system OXYZ is given by the vector r = xi + yj + zk ( 4.3 ) where i , j , k are , respectively , unit vectors along the X , Y ...
... vector spaces . As a starting point , recall that the position of a particle in a given cartesian coordinate system OXYZ is given by the vector r = xi + yj + zk ( 4.3 ) where i , j , k are , respectively , unit vectors along the X , Y ...
Página 53
... vectors in an n - dimensional vector 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 ...
... vectors in an n - dimensional vector 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 ...
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