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 m1 in the determinant | M ' | . Substitution into the ... coefficient of m1 in the expansion of this minor is M ' ] . The co- efficient of mm , is the negative of the ...
... coefficients on the left of ( 1A.10 ) and M is the cofactor of m1 in the determinant | M ' | . Substitution into the ... coefficient of m1 in the expansion of this minor is M ' ] . The co- efficient of mm , is the negative of the ...
Contenido
34 | 12 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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approximate arbitrary asymptotic ax² base vectors basis Bessel functions boundary conditions Chap coefficients consider constant continuous systems contour corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation eigen eigencolumns eigenfunctions eigenvalue problem eigenvectors elements evaluate expansion finite number follows formula given Green's function Hence Hermitian matrix Hermitian operator infinite integral representation integral theorem inverse Laplace transform linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company method multiplication nonsingular normal matrix obtained orthonormality conditions perturbation procedure relations result Ritz method satisfies scattering sinh solution solve spherical substitution transformation functions trial functions vanish variable vector space Verify wave whence write written x₁ y₁ yields York zero ηπχ παχ ди ду дх