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--- cwf:conditional_wave_function [2016/10/27 14:24] – markus
+++ cwf:conditional_wave_function [2016/10/30 17:33] (current) – markus
@@ Line 1: / Line 1: @@
 ====== The conditional wave function ======
-The concept was apparently introduced in [(:cite:cwf:DGZ1992)] and is given by the full wave function $\Psi$ of a system with some coordinates fixed at the position of the Bohmian trajectories for some fixed initial position. Thus it is possible to define the notion of the wave function of a subsystem with coordinates $x$, with the rest of the system described in coordinates $y$. If we assume the coordinates $y$ following the [[Bohmian trajectory]] $Y(t)$ in time then the conditional wave function of the subsystem is
+The concept was apparently introduced in [(:cite:cwf:DGZ1992)] and is given by the full wave function $\Psi$ of a system with some coordinates fixed at the position of the Bohmian trajectories for a given initial position. Thus it is possible to define the notion of the wave function of a subsystem with coordinates $x$, with the rest of the system described in coordinates $y$. If we assume the coordinates $y$ following the [[Bohmian trajectory]] $Y(t)$ in time then the conditional wave function of the subsystem is
 \begin{equation}
@@ Line 10: / Line 10: @@
 If the subsystems under consideration are non-entangled and also no assumed interaction leads to entanglement afterwards then it is shown that the conditional wave functions just obey seperate Schrödinger equations. Take $\Psi(t,x_1,x_2) = \alpha(t,x_1)\otimes\beta(t,x_2)$ and a potential $V_1(t,x_1)+V_2(t,x_2)$ (no interaction term). Then putting this into Schrödinger's equation
-\[
+\begin{equation}
 \mathrm{i}\hbar \partial_t \Psi = \left(-\frac{\hbar^2}{2m}(\Delta_1+\Delta_2) + V_1 + V_2\right)\Psi
-\]
+\end{equation}
 yields
 \begin{equation}