Add draft abstract and conclusion.

latex/sections/abstract.tex

@@ -2,6 +2,17 @@
 
 \begin{document}
 \begin{abstract}
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+We have simulated the two-dimensional time-dependent Schrödinger equation, to study 
+variations of the double-slit experiment. To solve the partial differential equations 
+we have applied the Crank-Nicolson scheme in 2+1 dimensions, to derive a discretized 
+equation. In addition, we have used Dirichlet boundary conditions to express the 
+equation in matrix form and solve it using the sparse matrix solver \verb|superlu|. 
+Our implementation, and choice of solver method, resulted in conserved total 
+probability $\sum_{\ivec, \jvec} p_{\ivec, \jvec}^{n}=1$ for both the single and 
+double slit setup. To illustrate the time evolution of the probability function, 
+we created colormap plots at time steps $t = [0, 0.001, 0.002]$. We also included 
+separate plots for each time step of Re$(u_{\ivec, \jvec})$ and Im$(u_{\ivec, \jvec})$.
+In addition, we determined the normalized particle detection probability $p(y \ | \ x=0.8, t=0.002)$, 
+for single-, double- and triple-slit.
 \end{abstract}
 \end{document}