Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 53
... basis . For convenience , this basis will be called the " u , basis " rather than by the more cumbersome expression , " the basis in which the U¿ are the base vectors . " A length may be defined for the vector x . This length should ( 1 ) ...
... basis . For convenience , this basis will be called the " u , basis " rather than by the more cumbersome expression , " the basis in which the U¿ are the base vectors . " A length may be defined for the vector x . This length should ( 1 ) ...
Página 60
... basis it is represented by sLs + , where s is the matrix which effects the transformation from the v , basis to the u , basis . Similarly , if + = ΣuLu * , then i , j L + = Σ ▽ x Σ $ xsL } e $ im ) ▽ m = k , m i , j = Σ vx ( SL * s ...
... basis it is represented by sLs + , where s is the matrix which effects the transformation from the v , basis to the u , basis . Similarly , if + = ΣuLu * , then i , j L + = Σ ▽ x Σ $ xsL } e $ im ) ▽ m = k , m i , j = Σ vx ( SL * s ...
Página 267
... basis λ . On transformation to another basis , say the μ basis , the expression for > becomes | > = \ μ > < μ | λ2 > < 2 | > ( 2B.2 ) in which denotes the base kets and < u > is the transformation function for the change from the λ basis ...
... basis λ . On transformation to another basis , say the μ basis , the expression for > becomes | > = \ μ > < μ | λ2 > < 2 | > ( 2B.2 ) in which denotes the base kets and < u > is the transformation function for the change from the λ basis ...
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