Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 158
... 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 ) Hm = - ' ( l + m ) ...
... 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 ) Hm = - ' ( l + m ) ...
Página 164
... spherical harmonics Y , " ( 0,9 ) . 5. Verify that z , ( p ) = √π / 2p Z1 + 1⁄21⁄2 ( P ) . 6. Find the 10 lowest ... Spherical , Cylindrical , and Ellip- soidal Harmonics , " Ginn and Company , Boston , 1893 . MacRobert , T. M ...
... spherical harmonics Y , " ( 0,9 ) . 5. Verify that z , ( p ) = √π / 2p Z1 + 1⁄21⁄2 ( P ) . 6. Find the 10 lowest ... Spherical , Cylindrical , and Ellip- soidal Harmonics , " Ginn and Company , Boston , 1893 . MacRobert , T. M ...
Página 299
... spherical harmonics , 153 Parodi , M. , 49 Partial waves , method of , 185-188 Pass method , 288 Pauling , L. , 224 ... spherical functions , 157 for spherical harmonics , 158-159 Residues , theorem of , 259-260 Ritz , W. , 215 Ritz ...
... spherical harmonics , 153 Parodi , M. , 49 Partial waves , method of , 185-188 Pass method , 288 Pauling , L. , 224 ... spherical functions , 157 for spherical harmonics , 158-159 Residues , theorem of , 259-260 Ritz , W. , 215 Ritz ...
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