\begin{landscape}
	\chapter{Übersicht und Notation}
	\begin{tabular}{l||l|l|l}
		& $d = 1$ & $d = 2$ & $d = 3$ \\ \hline \hline
		SG: $i\hbar \ket{\psi} = H \ket{\psi}$ &
			$\checkmark$ &
				$\checkmark$ &
					$\checkmark$ \\ \hline
		Hamiltonoperator: $H$ &
			$\frac{\hat{p}^2}{2m} + V(\hat{x})$ &
			$\frac{\hat{p}_x^2}{2m} + \frac{\hat{p}_y^2}{2m} + V(\hat{x}, \hat{y})$ &
			$\frac{\hat{p}_x^2}{2m} + \frac{\hat{p}_y^2}{2m} + \frac{\hat{p}_z^2}{2m} + V(\hat{x}, \hat{y}, \hat{z})$ \\ \hline
		Kommutator &
			$[\hat{x}, \hat{y}] = i\hbar$ &
			$[\hat{x}_k, \hat{y}_l] = i\hbar \krondelta{k,l};~ k, l = 1, 2$ &
			$[\hat{x}_k, \hat{y}_l] = i\hbar \krondelta{k,l};~ k, l = 1, 2, 3$ \\ \hline
			stationäre SG: $H \ket{\phi} = E \ket{\psi}$ &
			gewöhnliche DGL &
			partielle DGL &
			partielle DGL\\ \hline
		Rotationsinvarianz &
			Irrelevant &
			$V(x,y) = V(\rho)$; $\rho \equiv \sqrt{x^2 + y^2}$ &
			$V(x,y,z) = V(r)$; $r \equiv \sqrt{x^2 + y^2 + z^2}$ \\ \hline
		Ortseingen-vektoren &
			$\hat{x}\ket{x} = x \ket{x}$ &
			$\ket{x,y} \cequiv \ket{\rho, \theta}$ &
			$\ket{x,y,z} \cequiv \ket{\rho, \theta, \varphi}$ \\ \hline
		Norm der Wellenfunktion &
			\begin{math}1 = \intgr{-\infty}{+\infty}{\abs{\psi(x)}^2}{x}\end{math} &
			$\begin{array}{l}
				1 = \intgr{-\infty}{+\infty}{\intgr{-\infty}{+\infty}{\abs{\psi(x,y)}^2}{y}}{x} \\
				\hphantom{1} = \intgr{0}{\infty}{\rho \intgr{0}{2\pi}{\abs{\psi(\rho, \varphi)}^2}{\varphi}}{\rho}
			\end{array}$ &
			$\begin{array}{l}
				1 = \intgru{\intgru{\intgru{\abs{\psi(x,y,z)}^2}{x}}{y}}{z} \\
				\hphantom{1} = \intgr{0}{+\infty}{r^2 \intgr{-1}{+1}{\intgr{0}{2\pi}{\abs{\psi}^2}{\varphi}}{(\cos\theta)}}{r}
			\end{array}$ \\ \hline
	\end{tabular}
\end{landscape}
