Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 213
... demonstrated . It has therefore been proven that λ as defined by ( 15.3 ) is not less than the lowest eigenvalue of the operator . In a like manner , it may be demonstrated that is not greater than the highest eigenvalue of H. As an ...
... demonstrated . It has therefore been proven that λ as defined by ( 15.3 ) is not less than the lowest eigenvalue of the operator . In a like manner , it may be demonstrated that is not greater than the highest eigenvalue of H. As an ...
Página 248
... 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 the order of summation , or by ( 1A.5 ) and ( 1A.7 ) ...
... 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 the order of summation , or by ( 1A.5 ) and ( 1A.7 ) ...
Página 249
... demonstrated that | M | 0 is a sufficient con- dition for a system of n nonhomogeneous linear equations in n ... demonstrates necessity . - For convenience in consideration of sufficiency , let us now introduce the idea of rank of a ...
... demonstrated that | M | 0 is a sufficient con- dition for a system of n nonhomogeneous linear equations in n ... demonstrates necessity . - For convenience in consideration of sufficiency , let us now introduce the idea of rank of a ...
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