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- W2034650740 abstract "A variational formalism for the determination of the spinless single-particle density matrix $ensuremath{gamma}(stackrel{ensuremath{rightarrow}}{mathrm{r}}, {stackrel{ensuremath{rightarrow}}{mathrm{r}}}^{ensuremath{'}})$ for an interacting many-particle system, correct to second order, is developed. The method is based on variational principles for determining single-particle expectation values, correct to second order, without requiring highly accurate wave functions in order to represent the interacting system. The expectation value of the operator $X=Y+iZ$, where $Y=(frac{1}{2}){ensuremath{Sigma}}_{j}[W({stackrel{ensuremath{rightarrow}}{mathrm{r}}}_{i}){T}_{j}(stackrel{ensuremath{rightarrow}}{mathrm{a}})+W({stackrel{ensuremath{rightarrow}}{mathrm{r}}}_{j}^{ensuremath{'}}){T}_{j}(ensuremath{-}stackrel{ensuremath{rightarrow}}{mathrm{a}})]$, $Z=ensuremath{-}(frac{i}{2}){ensuremath{Sigma}}_{j}[W({stackrel{ensuremath{rightarrow}}{mathrm{r}}}_{j}){T}_{j}(stackrel{ensuremath{rightarrow}}{mathrm{a}})ensuremath{-}W({stackrel{ensuremath{rightarrow}}{mathrm{r}}}_{j}^{ensuremath{'}}){T}_{j}(ensuremath{-}stackrel{ensuremath{rightarrow}}{mathrm{a}})]$, $W({stackrel{ensuremath{rightarrow}}{mathrm{r}}}_{j})=ensuremath{delta}({stackrel{ensuremath{rightarrow}}{mathrm{r}}}_{j}ensuremath{-}stackrel{ensuremath{rightarrow}}{mathrm{r}})$, ${T}_{j}(stackrel{ensuremath{rightarrow}}{mathrm{a}})$ is a translation operator, and $stackrel{ensuremath{rightarrow}}{mathrm{a}}={stackrel{ensuremath{rightarrow}}{mathrm{r}}}^{ensuremath{'}}ensuremath{-}stackrel{ensuremath{rightarrow}}{mathrm{r}}$, is the reduced single-particle density matrix. For a given choice of a Slater-determinant-type trial wave function it is shown that the density matrix may be obtained from the charge density of the system where the latter too is determined via the same formalism to second order as the expectation value of the operator $W$ employing the same system trial wave function. The applicability of the technique is then demonstrated by showing that for the model hydrogen-atom problem it leads to highly accurate results for the momentum density and the Compton profile in the impulse approximation, and that the virial theorem is closely satisfied, even when the calculations of the various properties employing an approximate trial wave function alone are substantially in error." @default.
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- W2034650740 date "1975-02-01" @default.
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- W2034650740 title "Variational principles for the determination of single-particle density matrices" @default.
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- W2034650740 doi "https://doi.org/10.1103/physreva.11.409" @default.
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