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
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
Derechos de autor | |
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Términos y frases comunes
analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх