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 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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approximate arbitrary asymptotic ax² base vectors basis Bessel functions boundary conditions Chap coefficients consider constant continuous systems contour corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation eigen eigencolumns eigenfunctions eigenvalue problem eigenvectors elements evaluate expansion finite number follows formula given Green's function Hence Hermitian matrix Hermitian operator infinite integral representation integral theorem inverse Laplace transform linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company method multiplication nonsingular normal matrix obtained orthonormality conditions perturbation procedure relations result Ritz method satisfies scattering sinh solution solve spherical substitution transformation functions trial functions vanish variable vector space Verify wave whence write written x₁ y₁ yields York zero ηπχ παχ ди ду дх