https://mage.uber.space/dokuwiki/ 2026-05-03T18:51:13+00:00 https://mage.uber.space/dokuwiki/ https://mage.uber.space/dokuwiki/lib/tpl/dokuwiki/images/favicon.ico text/html 2023-11-22T12:53:42+00:00 Anonymous (anonymous@undisclosed.example.com) https://mage.uber.space/dokuwiki/forcebalance/calculation?rev=1700654022&do=diff List of all calculations Can I get a tree view of all calculation pages? Either here and/or on the calculation pages I should cite the page where it was used. Additionaly, i should refere to the definitions and assumptions. * EoM fermionic field operator * EoM particle number operator * EoM current density operator text/html 2023-11-21T14:24:02+00:00 Anonymous (anonymous@undisclosed.example.com) https://mage.uber.space/dokuwiki/forcebalance/definitions?rev=1700573042&do=diff List of important definitions * Current Density Operator text/html 2023-11-21T14:03:44+00:00 Anonymous (anonymous@undisclosed.example.com) https://mage.uber.space/dokuwiki/forcebalance/equation_of_moiton?rev=1700571824&do=diff DeleteMe text/html 2023-11-22T12:42:49+00:00 Anonymous (anonymous@undisclosed.example.com) https://mage.uber.space/dokuwiki/forcebalance/equation_of_motion?rev=1700653369&do=diff Equation of motion The equations of motion are derived here with the help of the Heisenberg EoM. Starting in the Heisenberg picture the time evolution of an operator is \begin{equation} \frac{\partial}{\partial t} \hat{O}_\text{H} (x,t) = \left[ \hat{O}_\text{H} (x,t) , \hat{H}_\text{H} (t) \right] + \left( \frac{\partial}{\partial t} \hat{O}_\text{S} (x) \right)_\text{H} \quad . \end{equation} Fermionic Field Operator The EoM for the electronic creation and anni… text/html 2023-11-22T12:50:17+00:00 Anonymous (anonymous@undisclosed.example.com) https://mage.uber.space/dokuwiki/forcebalance/force_based_formulation?rev=1700653817&do=diff Force Based Formulation -SUMMARY NODE- Overview of the theorem nodes: * Hamiltonian: Electron in external scalar Field * HK I + II * KS * equation of motion * Hartree functional * Exchange functional * Correlation functional text/html 2023-11-22T10:57:14+00:00 Anonymous (anonymous@undisclosed.example.com) https://mage.uber.space/dokuwiki/forcebalance/start?rev=1700647034&do=diff Force-Balance Approach To Functional Approximations The purpose of this wiki is to create a more or less consistent nomenclature within this project for all participants. Additionally, this is a way to create a collection of relevant sources: * Framework of the project\begin{equation} \hat{H} (t) = \hat{H}_0 (t) + H_{\text{int}} (t) \end{equation}$V(r,t)$\begin{equation} H_0 (t) = \sum_{\sigma^\prime, \sigma^{\prime\prime}} \int \!\mathrm{d}r^\prime \hat{\Psi}^{\dagger}(\vec{… text/html 2023-11-21T14:00:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://mage.uber.space/dokuwiki/forcebalance/theorems?rev=1700571629&do=diff List of Theorems * Equation of Motion