Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
Dentro del libro
Resultados 1-3 de 12
Página 54
... derived as follows : Multiply ( 4.6 ) by u ; + from the left . Then u * x = Σuƒux ; = x , Substitute for the x , in ( 4.6 ) by means of this result . Then X = n n X Σu , x ; = Σu , u , * x j = 1 n j = 1 X = Σuu + x i = 1 which states ...
... derived as follows : Multiply ( 4.6 ) by u ; + from the left . Then u * x = Σuƒux ; = x , Substitute for the x , in ( 4.6 ) by means of this result . Then X = n n X Σu , x ; = Σu , u , * x j = 1 n j = 1 X = Σuu + x i = 1 which states ...
Página 158
... derived in Sec . 11.8 , where are also derived some useful expansion formulae . 11.7 Recurrence Relations for the Spherical Harmonics It has already been seen in Sec . 11.4 that the normalized spherical harmonics Y , ( 0,9 ) satisfy the ...
... derived in Sec . 11.8 , where are also derived some useful expansion formulae . 11.7 Recurrence Relations for the Spherical Harmonics It has already been seen in Sec . 11.4 that the normalized spherical harmonics Y , ( 0,9 ) satisfy the ...
Página 160
... derived . In order to do this it is convenient to first derive some useful expansion formulae . The expansion of a plane wave1 er , traveling in an arbitrary direction a , ß ( i.e. , k has components k2 k sin a cos ẞ , k , k cos α ) is ...
... derived . In order to do this it is convenient to first derive some useful expansion formulae . The expansion of a plane wave1 er , traveling in an arbitrary direction a , ß ( i.e. , k has components k2 k sin a cos ẞ , k , k cos α ) is ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
Otras 19 secciones no mostradas
Otras ediciones - Ver todas
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