Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 54
Gerald Goertzel, Nunzio Tralli. bi - orthonormal basis . The relation ( 4.8 ) is known as the bi - orthonormality condition . If u ; * = u1 , all i , the basis is said to be orthonormal and the relation ( 4.8 ) is then known as the ...
Gerald Goertzel, Nunzio Tralli. bi - orthonormal basis . The relation ( 4.8 ) is known as the bi - orthonormality condition . If u ; * = u1 , all i , the basis is said to be orthonormal and the relation ( 4.8 ) is then known as the ...
Página 55
... orthonormal bases . A similar change of coordinates may be introduced in an n - dimensional vector space . Thus , suppose u , and v ... orthonormality of v , leads to d VECTOR SPACES AND LINEAR OPERATORS 555 Change of Basis Linear Operators.
... orthonormal bases . A similar change of coordinates may be introduced in an n - dimensional vector space . Thus , suppose u , and v ... orthonormality of v , leads to d VECTOR SPACES AND LINEAR OPERATORS 555 Change of Basis Linear Operators.
Página 272
... orthonormality conditions 1 +00 8 ( 0 - 0 ' ) - Sn , n ' = Σein ( 0-0 ) 2π n = -∞ 1 + x e - i ( n - n ' ) do 2π -R ( 2B.31 ) By using the relations ( 2B.7 ) and ( 2B.8 ) and the notation < 0 | > = f ( 0 ) and < n > = √√2a , we obtain ...
... orthonormality conditions 1 +00 8 ( 0 - 0 ' ) - Sn , n ' = Σein ( 0-0 ) 2π n = -∞ 1 + x e - i ( n - n ' ) do 2π -R ( 2B.31 ) By using the relations ( 2B.7 ) and ( 2B.8 ) and the notation < 0 | > = f ( 0 ) and < n > = √√2a , we obtain ...
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