Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 33
... normal coordinates . " A solution in which all v , but one are zero is called a normal mode . Thus , the jth normal mode is given by u ( t ) = S ̧ , v , ( 1 ) = S. , v , ( 0 ) e11 For the problem of Sec . 2.3 , as just considered , the ...
... normal coordinates . " A solution in which all v , but one are zero is called a normal mode . Thus , the jth normal mode is given by u ( t ) = S ̧ , v , ( 1 ) = S. , v , ( 0 ) e11 For the problem of Sec . 2.3 , as just considered , the ...
Página 64
... normal matrices . Furthermore , any real symmetric matrix is a normal matrix , since such a matrix can be considered as a special case of a Hermitian matrix . = Any matrix U such that U + U - 1 , or equivalently , U + U = UU + = 1 is ...
... normal matrices . Furthermore , any real symmetric matrix is a normal matrix , since such a matrix can be considered as a special case of a Hermitian matrix . = Any matrix U such that U + U - 1 , or equivalently , U + U = UU + = 1 is ...
Página 298
... Normal coordinate , 33 Normal matrix , 64 Normal mode , 33 Normal operator , 61 Null matrix , 11 Numerical methods , 236-242 Oberhettinger , F. , 145 , 294 Operator , adjoint , 60 , 103 in continuous systems , 96-110 , 132-135 a + , 132 ...
... Normal coordinate , 33 Normal matrix , 64 Normal mode , 33 Normal operator , 61 Null matrix , 11 Numerical methods , 236-242 Oberhettinger , F. , 145 , 294 Operator , adjoint , 60 , 103 in continuous systems , 96-110 , 132-135 a + , 132 ...
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