Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 54
... orthonormality condition . If u ; + = u1 , all i , the basis is said to be orthonormal and the relation ( 4.8 ) is then known as the orthonormality condition . The expression ( 4.8 ) then states that ( 1 ) the vectors u , are unitary ...
... orthonormality condition . If u ; + = u1 , all i , the basis is said to be orthonormal and the relation ( 4.8 ) is then known as the orthonormality condition . The expression ( 4.8 ) then states that ( 1 ) the vectors u , are unitary ...
Página 162
Gerald Goertzel, Nunzio Tralli. In order to derive the orthonormality condition satisfied by the func- tions j¿ ( kr ) Y , TM ( 0,9 ) note that the functions er satisfy the orthonor- mality condition - = i.e. , d ( x - x ' ) dy y ' ) 8 ...
Gerald Goertzel, Nunzio Tralli. In order to derive the orthonormality condition satisfied by the func- tions j¿ ( kr ) Y , TM ( 0,9 ) note that the functions er satisfy the orthonor- mality condition - = i.e. , d ( x - x ' ) dy y ' ) 8 ...
Página 299
... Orthonormality condition , 54 for spherical harmonics , 153 Parodi , M. , 49 Partial waves , method of , 185-188 Pass method , 288 Pauling , L. , 224 Periodic structures , 73-80 Perturbation of eigenvalues , 201-208 for degenerate ...
... Orthonormality condition , 54 for spherical harmonics , 153 Parodi , M. , 49 Partial waves , method of , 185-188 Pass method , 288 Pauling , L. , 224 Periodic structures , 73-80 Perturbation of eigenvalues , 201-208 for degenerate ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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