Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 15
... coefficients is not zero . 3. A set of n homogeneous equations in n unknowns has a nontrivial solution if and only if the determinant of the matrix of coefficients is zero . A nontrivial solution is one in which not all the unknowns ...
... coefficients is not zero . 3. A set of n homogeneous equations in n unknowns has a nontrivial solution if and only if the determinant of the matrix of coefficients is zero . A nontrivial solution is one in which not all the unknowns ...
Página 248
... coefficients | M | is unequal to zero . Thus we demonstrate the existence of a solution when | M | 0 by construction . Multiply the ith equation of ( 1A.8 ) by Mix , the cofactor of mix , and the sum over all i . Then , interchanging ...
... coefficients | M | is unequal to zero . Thus we demonstrate the existence of a solution when | M | 0 by construction . Multiply the ith equation of ( 1A.8 ) by Mix , the cofactor of mix , and the sum over all i . Then , interchanging ...
Página 250
... coefficients on the left of ( 1A.10 ) and M is the cofactor of mix in the determinant | M ' | \ . Substitution into ... coefficient of m1 in the expansion of this minor is [ M ' ] . The co- efficient of mim is the negative of the ...
... coefficients on the left of ( 1A.10 ) and M is the cofactor of mix in the determinant | M ' | \ . Substitution into ... coefficient of m1 in the expansion of this minor is [ M ' ] . The co- efficient of mim is the negative 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