Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 14
... properties of determinants which will be needed in Sec . 1.8 are summarized in Sec . 1.7 . 1.7 Some Properties of Determinants The determinant of a square matrix m is a number indicated as ❘m , read " determinant of m . " This ...
... properties of determinants which will be needed in Sec . 1.8 are summarized in Sec . 1.7 . 1.7 Some Properties of Determinants The determinant of a square matrix m is a number indicated as ❘m , read " determinant of m . " This ...
Página 134
... properties of these functions are discussed in subsequent sections of the text and in Appendix 2C . For our present purposes we require only the property J ( —wr ) = ( −1 ) ˆJ ( or ) , which allows us to consider ∞ in the range of ...
... properties of these functions are discussed in subsequent sections of the text and in Appendix 2C . For our present purposes we require only the property J ( —wr ) = ( −1 ) ˆJ ( or ) , which allows us to consider ∞ in the range of ...
Página 246
... properties III and IV , it follows that the value of a determinant is zero if any two rows ( or columns ) have corresponding elements propor- tional . V. If all the elements of any row ( or column ) are zero , the value of the ...
... properties III and IV , it follows that the value of a determinant is zero if any two rows ( or columns ) have corresponding elements propor- tional . V. If all the elements of any row ( or column ) are zero , the value of the ...
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