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Масса полезных советов, адреса и телефоны отелей и ресторанов, карта Гаваны и другая необходимая туристу информация.

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Spin Structure of p 33 l then />i or b(\)T + Σ * ( 0 Γ = λ,Γ (4-13) Tb(0 (4-14) />ι Similarly Tb(V) + Σ = λ,Γ />ι But 2 ΤΓ^6(Ι)Γ = Consequently, subtracting ΤΓ^Γ6(Ι) 2 from (4-14) (4-13) for / Φ 1 (4-15) gives [b, Ρ , ] = 0 (4-16) From ( 4 - 1 6 ) it follows that p is block diagonal in any basis set f that consists of eigenfunctions of b. There are several interesting operators of this type. For example if x t S | * > = Μ\Ψ) (4-17) z where §z = Σ s (0 z /= 1 then the spin dependence of Clearly must be block diagonal in a and β, that is, P l ρ,(χ; χ') = p„(r; r > ( £ ) « ( 0 * + Ρ (Τ, τ')β(ξ)β(0* β Tr (4-18) = TV = N + Ν (4-19) N = Tv (4-20) ^ = Tr P l a β where a Poi (4-21) P j 8 Also M = Tr S z P l ( x ; χ') = ±(N a - Ν) β (4-22) so (4-23) Ν β = \Ν - M (4-24) and both N and Ν are integers.

The radial part of the natural orbitals can then be found from / ( r ; r')R {ry dr' = X R (r) 2 P/ nl nl In terms of the radial natural orbitals, Ρ, = Σ ( P t takes the form y R (r)R (rTP,(cos nl nl (4-67) nl nl Θ) (4-68) The quantity (21 + l ) r ( r ; r) is the radial density of electrons with angular momentum /. Because /^(cos θ)\ = 1, the charge density 2 P/ θ=0 Pt( ) = p ( ; ) = Σ ( r r t is independent of angle. r 2 / 4 * 1 ^Ριίη r) 42 4 Analytic Properties of the First-Order Reduced Density Matrix C .

This is also clear from the fact that if a legitimate ρ, = Σ \ Ι ϊ / ) ( ϊ / Ι 2 * I * X * I (where Ψ = 2 / Ψ&Ϊ)> ^en t h same pj could also be obtained from Σ ^ / Ι ^ / Χ ^ / Ι with Wj = Σ Ψ Ψ Ι / , Ψ \ Since the energy for a system of noninteracting particles is most often computed from a Hamiltonian of the form α/(ρ) + βν(τ), it is of interest to know the boundary conditions on p (r) and p (p). Every p (r) with p (r) > 0 and f p (r) dr = Ν is possible. This may be seen from the fact that by (2-44) it is possible to define a Ψ so that p = N/L inside a box of length L (and zero outside if the orbitals are defined to be e inside and zero outside).

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