Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 25
... arbitrary u , since the indicated multiplication can be carried out . Simi- larly , if the value of f ( A ) u is known for arbitrary u , f ( A ) may be considered a known matrix.1 As a result of these simple considerations , it is clear ...
... arbitrary u , since the indicated multiplication can be carried out . Simi- larly , if the value of f ( A ) u is known for arbitrary u , f ( A ) may be considered a known matrix.1 As a result of these simple considerations , it is clear ...
Página 67
... arbitrary bra or ket ( in the old language , any arbitrary vector ) in terms of the base bras or kets . Thus , the arbitrary ket | x > , corresponding to the arbitrary vector x in the old notation , becomes | x > = | i > < i | x > ( 5.3 ) ...
... arbitrary bra or ket ( in the old language , any arbitrary vector ) in terms of the base bras or kets . Thus , the arbitrary ket | x > , corresponding to the arbitrary vector x in the old notation , becomes | x > = | i > < i | x > ( 5.3 ) ...
Página 80
... arbitrary x and y may be considered a definition of M + , as is seen by writing the equation in detailed form = 0 = ΣΜ - ΣΜήνα , i , j i , j = i , j Since y1 , x , are arbitrary , one has which indeed defines M + . - Mi ; = M2 + ji j ...
... arbitrary x and y may be considered a definition of M + , as is seen by writing the equation in detailed form = 0 = ΣΜ - ΣΜήνα , i , j i , j = i , j Since y1 , x , are arbitrary , one has which indeed defines M + . - Mi ; = M2 + ji j ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх