/*! \page OBDMDoc one-body density matrix Keyword: OBDM \section description Description Spherically averaged one-body density matrix for up-spin electrons \f$ \rho_{1\uparrow}^{sph}(|{\bf r}|) \f$, \f[ \rho_{1\uparrow}({\bf r}_1,{\bf r}_1') =\int d^3r_2\ldots d^3r_N\, \Psi^*({\bf r}_1,{\bf r}_2,\ldots,{\bf r}_N) \Psi({\bf r}_1',{\bf r}_2,\ldots,{\bf r}_N)\,, \f] \f[ \rho_{1\uparrow}^{sph}(|{\bf r}|) = \frac1{4\pi}\int d\Omega_{\bf r}\, \int d^3r_1 \rho_{1\uparrow}({\bf r}_1+{\bf r},{\bf r}_1)\,, \f] calculated on a one-dimensional grid. The many-body wave function \f$ \Psi \f$ in the above definition is assumed normalized to unity. Normalization of the density matrix is chosen so that \f$ \rho_{1\uparrow}^{sph}(0)=1 \f$. In homogeneous and isotropic systems, such as homogeneous electron gas, the one-body density matrix is a spherically symmetric function of only one distance, and therefore \f$ \rho_{1\uparrow}^{sph} \equiv \rho_{1\uparrow} \f$. In polarized cases, \f$ N_{\uparrow}\not = N_{\downarrow} \f$, the density matrix for down-electrons differs from the matrix for up-electrons. Quantity \f$ \rho_{1\downarrow}^{sph} \f$ is not (yet) implemented. \section options Options \subsection reqopt Required None. \subsection optopt Optional
OptionTypeDefaultDescription
CUTOFFFloat half of the smallest distance in the simulation cell Largest distance at which the density matrix is calculated. Values much larger than the default value have little physical meaning.
NGRIDInteger5 Number of points in the interval [0;CUTOFF] where the density matrix is calculated. The first point is CUTOFF/NGRID, the last point is CUTOFF.
AIPInteger1 Number of directions for spherical averaging using a Gaussian quadrature rule. Available are Gaussian rules with 4, 6, 12, 18, 26 and 32 points. Value AIP=1 disables spherical averaging and the vector \f$ \bf r \f$ then points in the x-direction.
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