Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 52
... relations ( 4.5 ) expresses the orthogonality ( i.e. , the mutual perpendicularity ) of the base vectors i , j , k . The second relation expresses the normality ( i.e. , the unit length ) of the base vectors . The relations ( 4.5 ) ...
... relations ( 4.5 ) expresses the orthogonality ( i.e. , the mutual perpendicularity ) of the base vectors i , j , k . The second relation expresses the normality ( i.e. , the unit length ) of the base vectors . The relations ( 4.5 ) ...
Página 118
... relations ( 9.17 ) becomes s ( x , w ) = = 2 ( w cos wx + sin x ) 0 < ∞ < ∞ ( 9.24 ) π ( 22 + w2 ) 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 ...
... relations ( 9.17 ) becomes s ( x , w ) = = 2 ( w cos wx + sin x ) 0 < ∞ < ∞ ( 9.24 ) π ( 22 + w2 ) 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 ...
Página 158
... Relations for the Spherical Harmonics It has already been seen in Sec . 11.4 that the normalized spherical harmonics Y , ( 0,9 ) satisfy the relations L + Y , m mym +1 = Z L_Y2m = H1mym - 1 in which = G , m √ ( 1 − m ) ( 1 + m + 1 ) ...
... Relations for the Spherical Harmonics It has already been seen in Sec . 11.4 that the normalized spherical harmonics Y , ( 0,9 ) satisfy the relations L + Y , m mym +1 = Z L_Y2m = H1mym - 1 in which = G , m √ ( 1 − m ) ( 1 + m + 1 ) ...
Contenido
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
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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