Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 101
... Substitution of ( 8.18 ) into ( 8.19 ) yields f ( x ) = [ [ ft ( x , y ) s ( v , x ' ) dy ] f ( x ) dx ( 8.18 ) ( 8.18a ) ( 8.19 ) ( 8.19a ) ( 8.20 ) ( 8.20a ) or f = TSƒ It then follows that one must have t ( x , y ) s ( y , x ' ) dy ...
... Substitution of ( 8.18 ) into ( 8.19 ) yields f ( x ) = [ [ ft ( x , y ) s ( v , x ' ) dy ] f ( x ) dx ( 8.18 ) ( 8.18a ) ( 8.19 ) ( 8.19a ) ( 8.20 ) ( 8.20a ) or f = TSƒ It then follows that one must have t ( x , y ) s ( y , x ' ) dy ...
Página 118
... Substitution of the second of the relations ( 9.17 ) into ( 9.20 ) yields 00 No2 [ R e2iz dx S No2 = 1 -2λ Hence the second and third of the relations ( 9.17 ) may be written So ( x ) = √ - 2λe1x So ( x ) = 0 λ < 0 2 > 0 The ...
... Substitution of the second of the relations ( 9.17 ) into ( 9.20 ) yields 00 No2 [ R e2iz dx S No2 = 1 -2λ Hence the second and third of the relations ( 9.17 ) may be written So ( x ) = √ - 2λe1x So ( x ) = 0 λ < 0 2 > 0 The ...
Página 141
... Substitution into ( 10.7a ) then gives 2 Cin⋅ T ( r , 0,1 ) = ( 1 ) * Σ i " - " ( " ( ) Σ n , n ' × [ e 2π ∞ w dw Se de S r ' dr ' S do ' ̧ ̄aw21J „ ( wr ) Jn ' ( wr ' ) ein ( 0-4 ) ̧ ̄in ' ( 0 ′ − 4 ) T ( r ' , 0 ′ , 0 ) ] On ...
... Substitution into ( 10.7a ) then gives 2 Cin⋅ T ( r , 0,1 ) = ( 1 ) * Σ i " - " ( " ( ) Σ n , n ' × [ e 2π ∞ w dw Se de S r ' dr ' S do ' ̧ ̄aw21J „ ( wr ) Jn ' ( wr ' ) ein ( 0-4 ) ̧ ̄in ' ( 0 ′ − 4 ) T ( r ' , 0 ′ , 0 ) ] On ...
Contenido
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
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Términos y frases comunes
analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх