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
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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Términos y frases comunes
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