Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 52
... Note that the base vectors i , j , k are linearly independent : If r = 0 , then x = y = z = 0. Any vector in three - dimensional space may be expressed as a linear combination of the three base vectors i , j , k . Note further that the ...
... Note that the base vectors i , j , k are linearly independent : If r = 0 , then x = y = z = 0. Any vector in three - dimensional space may be expressed as a linear combination of the three base vectors i , j , k . Note further that the ...
Página 97
... Note that f ( 0 ) and ƒ ( n + 1 ) are auxiliary variables defined by these boundary conditions . 2 Note that the statement " is Hermitian " means either ( a ) L is a Hermitian matrix or ( b ) μ d2 with the boundary conditions ( 8.4 ) is ...
... Note that f ( 0 ) and ƒ ( n + 1 ) are auxiliary variables defined by these boundary conditions . 2 Note that the statement " is Hermitian " means either ( a ) L is a Hermitian matrix or ( b ) μ d2 with the boundary conditions ( 8.4 ) is ...
Página 120
... Note that MπT n ( 9.33 ) L i.e. , the eigenvalues are discrete . The normalization condition s1 ( x ) s , ( x ) dx = 1 ( 9.34 ) yields c - 2 = Hence , finally ηπα Sn ( x ) = < x \ n > = sin n = 1 , 2 , . . . L ( 9.35 ) In order to ...
... Note that MπT n ( 9.33 ) L i.e. , the eigenvalues are discrete . The normalization condition s1 ( x ) s , ( x ) dx = 1 ( 9.34 ) yields c - 2 = Hence , finally ηπα Sn ( x ) = < x \ n > = sin n = 1 , 2 , . . . L ( 9.35 ) In order to ...
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