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 2 s ( x , w ) = ( w cos wx + λ sin wx ) 0 < ∞ < ∞ ( 9.24 ) π ( 22 + w2 ) Substitution of the second of the relations ( 9.17 ) into ( 9.20 ) yields ∞ No S e21x dx = No2 -2λ = 1 Hence the second and third of ...
... relations ( 9.17 ) becomes 2 s ( x , w ) = ( w cos wx + λ sin wx ) 0 < ∞ < ∞ ( 9.24 ) π ( 22 + w2 ) Substitution of the second of the relations ( 9.17 ) into ( 9.20 ) yields ∞ No S e21x dx = No2 -2λ = 1 Hence the second and third of ...
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 = LY " GY + 1 in which Gm = L_Y , " H " Y " -1 = √ ( 1 − m ) ( 1 + m + 1 ) - H ...
... 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 = LY " GY + 1 in which Gm = L_Y , " H " Y " -1 = √ ( 1 − m ) ( 1 + m + 1 ) - H ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх