Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 88
... evaluate any function f ( 82 ) of the difference operator d2 it is necessary to find the eigencolumns and eigenvalues of 82 ( with its accom- panying boundary conditions ) . In so doing , the boundary conditions are an implicit part of ...
... evaluate any function f ( 82 ) of the difference operator d2 it is necessary to find the eigencolumns and eigenvalues of 82 ( with its accom- panying boundary conditions ) . In so doing , the boundary conditions are an implicit part of ...
Página 172
... evaluating the integral ( 12.33 ) or by solving the differential equation ( 12.35 ) . We shall evaluate the integral ( 12.33 ) and leave the solution of Eq . ( 12.35 ) as an exercise for the reader . Since the integrand in ( 12.33 ) is ...
... evaluating the integral ( 12.33 ) or by solving the differential equation ( 12.35 ) . We shall evaluate the integral ( 12.33 ) and leave the solution of Eq . ( 12.35 ) as an exercise for the reader . Since the integrand in ( 12.33 ) is ...
Página 263
... evaluate 41 = f +00 -∞ eizt dx x2 + a2 ( 2A.4 ) We note that the integrand has poles at z = ia . Ift > 0 the ... evaluating ∞ + eixt = dx ∞ X -x ( 2A.7 ) Clearly the integrand diverges when x = α and the integral is meaning- less ...
... evaluate 41 = f +00 -∞ eizt dx x2 + a2 ( 2A.4 ) We note that the integrand has poles at z = ia . Ift > 0 the ... evaluating ∞ + eixt = dx ∞ X -x ( 2A.7 ) Clearly the integrand diverges when x = α and the integral is meaning- less ...
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