Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 97
... the boundary conditions ( 8.4 ) is Hermitian . It is incorrect to omit the italic phrase . The boundary conditions are part of the definition of the operator . μ When an operator L is defined by ( 8.6 ) OPERATORS IN CONTINUOUS SYSTEMS 97.
... the boundary conditions ( 8.4 ) is Hermitian . It is incorrect to omit the italic phrase . The boundary conditions are part of the definition of the operator . μ When an operator L is defined by ( 8.6 ) OPERATORS IN CONTINUOUS SYSTEMS 97.
Página 98
... defined so that if g ( x ) = f ( x ) , then g ( x ) = d2 dx2 f ( x ) f ( 0 ) = f ( L ) = 0 These relations have an obvious similarity to ( 8.3 ) and ( 8.4 ) . ( 8.7 ) ( 8.8 ) That as defined in ( 8.7 ) and ( 8.8 ) cannot be readily put ...
... defined so that if g ( x ) = f ( x ) , then g ( x ) = d2 dx2 f ( x ) f ( 0 ) = f ( L ) = 0 These relations have an obvious similarity to ( 8.3 ) and ( 8.4 ) . ( 8.7 ) ( 8.8 ) That as defined in ( 8.7 ) and ( 8.8 ) cannot be readily put ...
Página 244
... define an n × n determinant . By definition | A | = Σ Ɛi ,, i ,, . . . ‚ i‚a1i‚a2iq · A nin ... a11 a12 a21 a22 ain ... defined by Ei = i ' € 1,2,3 , ... : 1 n = The sum in ( 1A.1 ) is over all n ! permutations . Stated otherwise , the ...
... define an n × n determinant . By definition | A | = Σ Ɛi ,, i ,, . . . ‚ i‚a1i‚a2iq · A nin ... a11 a12 a21 a22 ain ... defined by Ei = i ' € 1,2,3 , ... : 1 n = The sum in ( 1A.1 ) is over all n ! permutations . Stated otherwise , the ...
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