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 H. 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 H. 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 , Σ ( Σm ,, Mix ) x ; = Σ ...
... 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 , Σ ( Σm ,, Mix ) x ; = Σ ...
Página 249
... demonstrated that [ M ] # 0 is a sufficient con- dition for a system of ʼn 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 ʼn nonhomogeneous linear equations in n ... demonstrates necessity . For convenience in consideration of sufficiency , let us now introduce the idea of rank of a ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх