Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 9
... clear from context , one may write Σ . If the summation i n variable is clear but not the range of summation , one may write Σ . In many instances the unadorned symbol Σ suffices . Just as the name of the variable of integration does ...
... clear from context , one may write Σ . If the summation i n variable is clear but not the range of summation , one may write Σ . In many instances the unadorned symbol Σ suffices . Just as the name of the variable of integration does ...
Página 75
... clearly seen by examination of ( 6.5 ) ] , there exist matrices S and A ( A is diagonal with real elements ) such ... clear that Y1 = u ( x - 12x + x + 1 ) Y1 = u ( x2 - x1 ) - μgX1 ― Yn = μ ( Xn - 1 Xn ) μLXn i = 2 , ... , n - 1 By a ...
... clearly seen by examination of ( 6.5 ) ] , there exist matrices S and A ( A is diagonal with real elements ) such ... clear that Y1 = u ( x - 12x + x + 1 ) Y1 = u ( x2 - x1 ) - μgX1 ― Yn = μ ( Xn - 1 Xn ) μLXn i = 2 , ... , n - 1 By a ...
Página 142
... clear that the solutions to Eq . ( 10.55 ) are the eigenfunctions fx , n ( r , 0 ) = J ( kr ) eino ( 10.56 ) in which the Bessel functions must satisfy the boundary condition Jn ( kp ) = 0. This condition determines the eigenvalues as ...
... clear that the solutions to Eq . ( 10.55 ) are the eigenfunctions fx , n ( r , 0 ) = J ( kr ) eino ( 10.56 ) in which the Bessel functions must satisfy the boundary condition Jn ( kp ) = 0. This condition determines the eigenvalues as ...
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