Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 5
... discussed in Sec . 1.1 , it is desirable to introduce a uniform notation . A first step in this direction is carried out below . The problems discussed above may be divided into three categories : the time - dependent homogeneous prob ...
... discussed in Sec . 1.1 , it is desirable to introduce a uniform notation . A first step in this direction is carried out below . The problems discussed above may be divided into three categories : the time - dependent homogeneous prob ...
Página 225
... discussed below . 16.2 Eigenvalue Problems One of the first successful iteration methods , that due to Cayley- Sylvester , may be used in the case of discrete systems to determine the largest ( in magnitude ) eigenvalue and the ...
... discussed below . 16.2 Eigenvalue Problems One of the first successful iteration methods , that due to Cayley- Sylvester , may be used in the case of discrete systems to determine the largest ( in magnitude ) eigenvalue and the ...
Página 233
... discussed in Chaps . 14 to 16. In this chapter we shall show how some problems may be transformed into eigenvalue problems and , therefore , solved by the previously discussed methods . 17.2 The Method Suppose that one wishes to ...
... discussed in Chaps . 14 to 16. In this chapter we shall show how some problems may be transformed into eigenvalue problems and , therefore , solved by the previously discussed methods . 17.2 The Method Suppose that one wishes to ...
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