Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 129
... orthonormality conditions satisfied by these eigenfunctions are d ( x − x ' ) d ( y — y ' ) = < x , y | wx‚Wy > < wx‚wy | x'‚y ' > ¿ ( wx — w'1⁄2 ) d ( ∞ , — w ' ) = < wxw „ [ x , y > < x , y | w ' , „ , w % , > They require that A be ...
... orthonormality conditions satisfied by these eigenfunctions are d ( x − x ' ) d ( y — y ' ) = < x , y | wx‚Wy > < wx‚wy | x'‚y ' > ¿ ( wx — w'1⁄2 ) d ( ∞ , — w ' ) = < wxw „ [ x , y > < x , y | w ' , „ , w % , > They require that A be ...
Página 268
... orthonormality conditions ( 2B.5 ) - and ( 2B.6 ) , i.e. , d ( w — w ' ) = d ( x − x ' ) - - 1 2π 1 S + ∞ - ∞0 e ̄i ( w − ∞ ' ) x dx [ + e + ( x - x ) ∞ dw , 2π - 00 ( 2B.10 ) For example , we verify that 8 ( x - x ' ) = lim 2π a ...
... orthonormality conditions ( 2B.5 ) - and ( 2B.6 ) , i.e. , d ( w — w ' ) = d ( x − x ' ) - - 1 2π 1 S + ∞ - ∞0 e ̄i ( w − ∞ ' ) x dx [ + e + ( x - x ) ∞ dw , 2π - 00 ( 2B.10 ) For example , we verify that 8 ( x - x ' ) = lim 2π a ...
Página 271
... orthonormality conditions A ) T **** -∞ 818 2 + ∞ + - d ( w1wi ) d ( w2 — w2 ) = - − 8 ( X1 X1 ' ) 8 ( x2 − x2 ) = ― 2 + ∞ + ∞o ATT 918 e ̄i [ ( w1 − wí ) x1 + ( w2 − w1⁄2 ) x2 ] dx1 dx2 e + i [ ( x1 − xí ) ∞1 + ( x2 − xá ) ...
... orthonormality conditions A ) T **** -∞ 818 2 + ∞ + - d ( w1wi ) d ( w2 — w2 ) = - − 8 ( X1 X1 ' ) 8 ( x2 − x2 ) = ― 2 + ∞ + ∞o ATT 918 e ̄i [ ( w1 − wí ) x1 + ( w2 − w1⁄2 ) x2 ] dx1 dx2 e + i [ ( x1 − xí ) ∞1 + ( x2 − xá ) ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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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