Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 246
... expansion of the determinant may be separated into two terms , because each term contains one factor from the row ( or column ) whose elements are written as the sum of two numbers . Thus one has two expansions ( i.e. , two determinants ) ...
... expansion of the determinant may be separated into two terms , because each term contains one factor from the row ( or column ) whose elements are written as the sum of two numbers . Thus one has two expansions ( i.e. , two determinants ) ...
Página 247
... expansion of a determinant is known as the simple Laplace expansion . Consider the sum n Σdij Dki ki j = 1 Each term of this sum is the product of an element in the ith row of a determinant D❘ by the cofactor of the corresponding ...
... expansion of a determinant is known as the simple Laplace expansion . Consider the sum n Σdij Dki ki j = 1 Each term of this sum is the product of an element in the ith row of a determinant D❘ by the cofactor of the corresponding ...
Página 287
... Expansions A divergent series Got a1 a2 + + + + Z z2 in which the sum of the first ( n + 1 ) terms is S , ( z ) , is said to be an asymp- totic expansion of a function f ( z ) for a given range of values of arg z ( if z = re1o , 0 = arg ...
... Expansions A divergent series Got a1 a2 + + + + Z z2 in which the sum of the first ( n + 1 ) terms is S , ( z ) , is said to be an asymp- totic expansion of a function f ( z ) for a given range of values of arg z ( if z = re1o , 0 = arg ...
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