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
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