\documentclass[article,oldfontcommands]{memoir}
\usepackage{amsmath} %needed for \boldsymbol etc.
\usepackage{array} %needed for m{1.5cm} etc.
\usepackage[collision]{chemsym} %needed for $\C_6\H_5\Br$ etc.
\newcommand{\ket}[1]{\, |#1\rangle}
\newcommand{\bra}[1]{\langle #1 |\,}
\newcommand{\X}{\mathbf{X}}
\begin{document}
\begin{table}[htbp]
\centering
\begin{tabular}[c]{c}
\begin{tabular}{|c|cc|}
\hline
\bf Temperatur & \bf Iltforbrug (STPD) & \bf RQ \\
\hline
\hline
0 & 185 & 0,55 \\
0 & 178,4 & 0,55 \\
10 & 385,79 & 0,71 \\
18 & 837 & 0,4 \\
18 & 755 & 0,21 \\
30 & 1240 & 1 \\
30 & 1760,6 & 0,16 \\
\hline
\end{tabular}
\end{tabular}
\caption{Klassens resultater.}
\label{tab:RQ}
\end{table}
\begin{tabular}{||rccc||}
\hline
\rule{0pt}{10pt} & $\C_6\H_5\Br$ & $\Mg$ & $\C_6\H_5\Mg\Br$ \\
\hline
\hline
\rule{0pt}{10pt} M$_w$ : & $156,9$ mol g$^{-1}$ & $24,3$ mol g$^{-1}$ & $181,2$ mol g$^{-1}$\\
\rule{0pt}{10pt} m : & $9,9$ g & $1,35$ g & \\
\rule{0pt}{10pt} n : & $0.063$ mol & $0,055$ mol & $0,055$ mol \\
\hline
\hline
\rule{0pt}{10pt} & $(\C_6\H_5)_3\C\O\O\C\H_3$ & $(\C_6\H_5)_3\C\O\Mg\Br$ & $(\C_6\H_5)_3\C\O\H$ \\
\hline
\hline
\rule{0pt}{10pt} M$_w$ : & $135,98$ mol g$^{-1}$ & $363,19$ mol g$^{-1}$ & $259,99$ mol g$^{-1}$ \\
\rule{0pt}{10pt} m : & $3,5$ g & & $7,28$ g \\
\rule{0pt}{10pt} n : & $0,028$ mol & $\sim 0,028$ mol & $\sim 0,028$ mol \\
\hline
\end{tabular}
\begin{center}
\begin{tabular}{||l|c|c||}
\hline
\rule{0pt}{10pt} & {\bf Fundet} & {\bf Teoretisk}\\
\hline
\hline
\rule{0pt}{15pt} Udbytte: & 1,29~g (17\%) & 7.28~g\\
\rule{0pt}{15pt} Mp: & 156-57$^{\circ}$C & 157-59$^{\circ}$C\\
\hline
\end{tabular}
\end{center}
\begin{table}[ht]
\centering
\begin{tabular}{|c|c|}
\hline
\rule{0pt}{10pt} {\bf Vand} & \\
\hline
\hline
\rule{0pt}{10pt}
Volumen & $2\cdot 10^{-6}$ m$^3$ $\pm$ $5\cdot 10^{-7}$ m$^3$ \\
Antal dråber & 44 $\pm$ $0$ \\
$\gamma$ & $3.2\cdot 10^{-2}$ N m$^{-1}$ $\pm$ $8\cdot 10^{-3}$N m$^{-1}$\\
\hline
\hline
\rule{0pt}{10pt} {\bf Ethanol} & \\
\hline
\hline
\rule{0pt}{10pt}
Volumen & $2\cdot 10^{-6}$ m$^3$ $\pm$ $5\cdot 10^{-7}$ m$^3$ \\
Antal dråber & 99 $\pm$ $10$ \\
$\gamma$ & $1.5\cdot 10^{-2}$ N m$^{-1}$ $\pm$ $4\cdot 10^{-3}$N m$^{-1}$\\
\hline
\end{tabular}
\caption{Måleresultater af opsamlet volumen og antal dråber, og den Excel beregnede $\gamma$.}
\label{tab:draabedannelse.maalinger}
\end{table}
\begin{table}[ht]
\centering
\begin{tabular}{|r|r|}
\hline
$\boldsymbol{\gamma}$ & \\
\hline
\hline
\rule{0pt}{10pt}
Vand & $7.3\cdot 10^{-2}$ N M$^{-1}$ \\
Ethanol & $2.3\cdot 10^{-2}$ N M$^{-1}$ \\
\hline
\end{tabular}
\caption{Tabel værdierne for $\gamma$}
\label{tab:draabedannelse.tabel}
\end{table}
\begin{tabular}{rrr|rr|r}
\hline
$m$ & $l$ & $i$ & $\tau_\text{tot}=\tau+\tau_0$ & $\tau_B=B\mu$ & $\tau_B-\tau_\text{tot}=0$ \\
\hline
0.008 & 0.1 & 1.6 & 0.00873 & 0.0088 & 0.00007 \\
0.008 & 0.07 & 1.12 & 0.00637 & 0.00616 & -0.0002 \\
0.004 & 0.1 & 0.88 & 0.00480 & 0.00484 & 0.00004 \\
0.004 & 0.07 & 0.64 & 0.0036 & 0.00352 & -0.00011 \\
\hline
\end{tabular}
\begin{table}[htbp]
\centering
\begin{tabular}{m{1.5cm} m{2.5cm} m{2.5cm}}
\toprule
& $E>V$ & $E<V$ \\
\midrule
$\psi>0$: & curv-down.eps & curv-up.eps\\
$\psi<0$: & curv-up.eps & curv-down.eps\\
\bottomrule
\end{tabular}
\caption[Curvature of the wave function]{Curvature of the wave function.}
\label{tab:curvatire}
\end{table}
\begin{table}[htbp]
\centering
\begin{tabular}{lcccc}
\toprule
& Finite well & Infinite well & Harmonic potential & Triangle potential\\
\midrule
$\varepsilon_0$ & 1.891 & 2.467 & 0.499 & 0.396\\
$\varepsilon_1$ & 7.525 & 9.87 & 1.499 & 0.759\\
$\varepsilon_2$ & 16.767 & 22.2 & 2.499 & -\\
$\varepsilon_3$ & 29.286 & 39.48 & 3.499 & -\\
$\varepsilon_4$ & 44.035 & 61.69 & 4.499 & -\\
\bottomrule
\end{tabular}
\caption[Energies for the wave function in several potentials]{The energies for the finite and infinite square well potentials, the harmonic oscillator potential and the triangle potential, $\alpha=1/10$ in dimensionless units.}
\label{tab:energies-fin-inf-wells}
\end{table}
\begin{table}[htbp]
\centering
\begin{tabular}{lcc}
\toprule
\textbf{The Ground State:} & Finite well potential & Harmonic potential \\
\midrule
$f(\X) = \exp(-\beta \X^2)$ & 2.15 & 0.499 \\
$ f(\X) = \exp(-\beta |\X|)$ & 4.48 & 0.676 \\
$f(\X) = \cos(\beta \X)$ & 2.23 & 0.57 \\
The real wave function & 1.89 & 0.499 \\
\bottomrule
\end{tabular}
\caption[Variational results for the ground state of two potentials]{Variational results for the ground state of the finite well and the harmonic potential.}
\label{tab:variational}
\end{table}
\begin{table}[htbp]
\centering
\begin{tabular}{lcc}
\toprule
\textbf{The 1st Excited State:} & Finite well potential & Harmonic potential \\
\midrule
$f(\X) = \X\exp(-\beta \X^2)$ & 8.201 & 1.495 \\
$ f(\X) = \X\exp(-\beta |\X|)$ & 11.89 & 1.718 \\
$f(\X) = \X\cos(\beta \X)$ & 8.594 & 1.768 \\
The real wave function & 7.525 & 1.499 \\
\bottomrule
\end{tabular}
\caption[Variational results for the first excited state of two potentials]{Variational results for the first excited state of the finite well and the harmonic potential.}
\label{tab:variational-1}
\end{table}
\begin{table}[tb]
\centering
\begin{adjustwidth*}{-1.1in}{}
\begin{tabular}{ccccccccc}
\toprule
& & & $V_0= 2$ & & & $V_0= 5$ & & \\
\midrule
$\ket{n}$ & \multicolumn{ 2}{c}{Unperturbed Energy} & $\ket{n}$ & Perturbed & Exact & $\ket{n}$ & Perturbed & Exact \\
\midrule
0 & \multicolumn{ 2}{c}{1.890850495} & 0 & 2.68774062 & 2.6907607 & 0 & 3.75858678 & 3.74204499 \\
1 & \multicolumn{ 2}{c}{7.525078075} & 1 & 7.64143918 & 7.6451436 & 1 & 7.80645899 & 7.81253356 \\
2 & \multicolumn{ 2}{c}{16.76700317} & 2 & 17.4082279 & 17.402530 & 2 & 18.4941864 & 18.4413390 \\
3 & \multicolumn{ 2}{c}{29.28589643} & 3 & 29.7700256 & 29.626278 & 3 & 30.5057413 & 30.1160255 \\
4 & \multicolumn{ 2}{c}{44.03462731} & 4 & 44.3988388 & 44.378844 & 4 & 44.9455238 & 44.9274800 \\
\toprule
$V_0= 10$ & & & $V_0= 20$ & & & $V_0= 40$ & & \\
\midrule
$\ket{n}$ & Perturbed & Exact & $\ket{n}$ & Perturbed & Exact & $\ket{n}$ & Perturbed & Exact \\
\midrule
0 & 5.21135958 & 5.13244619 & 0 & 6.87201475 & 6.9024154 & 0 & 5.21376331 & 8.49850996 \\
1 & 8.05610043 & 8.06184361 & 1 & 8.46016486 & 8.4714451 & 1 & 8.88741995 & 9.05153551 \\
2 & 20.6351080 & 20.3479315 & 2 & 26.1581661 & 24.355128 & 2 & 42.1691413 & 30.6668117 \\
3 & 31.7573257 & 30.8782262 & 3 & 34.3557130 & 32.212670 & 3 & 39.9333613 & 34.2528377 \\
4 & 45.8576454 & 45.9342207 & 4 & 47.6855645 & 48.269748 & 4 & 51.3561050 & --- \\
\bottomrule
\end{tabular}
\end{adjustwidth*}
\caption[Numerical results for the perturbation method and the shooting method]{Numerical results for the energies obtained by the perturbation method and exact values by the shooting method for perturbations.}
\label{tab:perturb-calulations}
\end{table}\begin{table}[htbp]
\centering
\begin{adjustwidth*}{0in}{-0.9in}
\begin{tabular}{ccccccccc}
\toprule
$V_0=2$ & & & $V_0=10$ & & & $V_0=40$ & & \\
\midrule
$\ket{n}$ & 1st order & 2nd order & $\ket{n}$ & 1st order & 2nd order & $\ket{n}$ & 1st order & 2nd order \\
\midrule
0 & 2.72093770 & 2.68774062 & 0 & 6.04128654 & 5.21135958 & 0 & 18.4925947 & 5.21376331 \\
1 & 7.64397833 & 7.64143918 & 1 & 8.11957939 & 8.05610043 & 1 & 9.90308336 & 8.88741995 \\
2 & 17.3751288 & 17.4082279 & 2 & 19.8076315 & 20.6351080 & 2 & 28.9295167 & 42.1691413 \\
3 & 29.7674865 & 29.7700256 & 3 & 31.6938468 & 31.7573257 & 3 & 38.9176979 & 39.9333613 \\
4 & 44.3987408 & 44.3988388 & 4 & 45.8551950 & 45.8576454 & 4 & 51.3168983 & 51.3561050 \\
\bottomrule
\end{tabular}
\end{adjustwidth*}
\caption{Perturbation results for the energies $E_n$, calculated to first and second order.}
\label{tab:perturb-calulations-order-corrections}
\end{table}\begin{table}[htbp]
\begin{tabular}{cccc}
\toprule
$\ket{n}$ & Exact & Perturbed & Matrix \\
\midrule
0 & 7.990295595 & 8.00316575 & 8.003312 \\
1 & 8.572961234 & 8.57098177 & 8.571135 \\
\midrule
& \multicolumn{ 3}{l}{$E_0 = 8.28722344$} \\
& \multicolumn{ 3}{l}{$S \;\, = 0.02069867$} \\
& \multicolumn{ 3}{l}{$V' = \bra{\psi_\ell}V_r-V_0\ket{\psi_r} = -0.283911104$} \\
& \multicolumn{ 3}{l}{$\phantom{V' =\;}\bra{\psi_\ell}V_r-V_0\ket{\psi_\ell} \,= -0.006026201$}\\
\bottomrule
\end{tabular}
\caption{Energies for the double well potential.}
\label{tab:double-well-energies}
\end{table}\begin{table}[htbp]
\begin{tabular}{lcccccc}
\toprule
Number of wells & $\ket{n}$& & & & & \\
\midrule
2 & 0th & + & + & & & \\
& 1st & + & -- & & & \\
\midrule
3 & 0th & + & + & + & & \\
& 1st & + & 0 & -- & & \\
& 2nd & + & -- & + & & \\
\midrule
4 & 0th & + & + & + & + & \\
& 1st & + & + & -- & -- & \\
& 2nd & + & -- & -- & + & \\
& 3rd & + & -- & + & -- & \\
\midrule
5 & 0th & + & + & + & + & + \\
& 1st & + & + & 0 & -- & -- \\
& 2nd & + & 0 & -- & 0 & + \\
& 3rd & + & -- & 0 & + & -- \\
& 4th & + & -- & + & -- & + \\
\bottomrule
\end{tabular}
\caption[Signature of the wave functions in multiple wells.]{Signature of the wave functions in multiple wells. The curvature is positive in (+), negative in (-) and zero in (0).}
\label{tab:signature-multiple-wells}
\end{table}
\begin{table}[htbp]
\centering
\begin{tabular}{lccclccc}
\toprule
No. of wells & $\ket{n}$ & Exact & Matrix & No. of wells & $\ket{n}$ & Exact & Matrix \\
\midrule
3 & 0 & 7.87161719 & 7.88571251 & 4 & 0 & 7.81462248 & 7.82784563 \\
& 1 & 8.27250702 & 8.28722345 & & 1 & 8.09220791 & 8.11175673 \\
& 2 & 8.69529213 & 8.68873438 & & 2 & 8.45166881 & 8.46269016 \\
& -- & -- & -- & & 3 & 8.75700426 & 8.74660126 \\
\midrule
No. of wells & $\ket{n}$ & Exact & Matrix & No. of wells & $\ket{n}$ & Exact & Matrix \\
\midrule
5 & 0 & 7.78325035 & 7.79547499 & 6 & 0 & 7.76422927 & 7.77563331 \\
& 1 & 7.98349286 & 8.00331234 & & 1 & 7.91446488 & 7.93319209 \\
& 2 & 8.26761563 & 8.28722345 & & 2 & 8.13832688 & 8.16087112 \\
& 3 & 8.56508893 & 8.57113455 & & 3 & 8.39690368 & 8.41357577 \\
& 4 & 8.79213105 & 8.77897190 & & 4 & 8.63982438 & 8.64125480 \\
& -- & -- & -- & & 5 & 8.81393242 & 8.79881358 \\
\midrule
No. of wells & $\ket{n}$ & Exact & Matrix & No. of wells & $\ket{n}$ & Exact & Matrix \\
\midrule
7 & 0 & 7.75185864 & 7.76262413 & 8 & 0 & 7.74336892 & 7.75364511 \\
& 1 & 7.86829119 & 7.88571251 & & 1 & 7.83614993 & 7.85224640 \\
& 2 & 8.04708325 & 8.06992729 & & 2 & 7.98126001 & 8.00331234 \\
& 3 & 8.26518034 & 8.28722345 & & 3 & 8.16443872 & 8.18862215 \\
& 4 & 8.49179660 & 8.50451960 & & 4 & 8.36609476 & 8.38582474 \\
& 5 & 8.69115742 & 8.68873438 & & 5 & 8.56241882 & 8.57113455 \\
& 6 & 8.82835783 & 8.81182276 & & 6 & 8.72774422 & 8.72220049 \\
& -- & -- & -- & & 7 & 8.83838104 & 8.82080179 \\
\bottomrule
\end{tabular}
\caption[Energies for multiple well potentials.]{Energies for the several multiple well potentials. Calculated exact by the shooting method and by the matrix method eq.~(??).}
\label{tab:multiple-well-energies}
\end{table}
\begin{table}[htbp]
\centering
\begin{tabular}{lccccccccccc}
\toprule
Number of wells & $\ket{n}$ & & & & & & & & & & \\
\midrule
6 & 1st & + & + & + & + & + & + & & & & \\
& 2nd & + & + & + & -- & -- & -- & & & & \\
& 3rd & + & + & -- & -- & + & + & & & & \\
& 4th & + & -- & -- & + & + & -- & & & & \\
& 5th & + & -- & + & + & -- & + & & & & \\
& 6th & + & -- & + & -- & + & -- & & & & \\
\midrule
7 & 1st & + & + & + & + & + & + & + & & & \\
& 2nd & + & + & + & 0 & -- & -- & -- & & & \\
& 3rd & + & + & -- & -- & -- & + & + & & & \\
& 4th & + & 0 & -- & 0 & + & 0 & -- & & & \\
& 5th & + & -- & -- & + & -- & -- & + & & & \\
& 6th & + & -- & + & 0 & -- & + & -- & & & \\
& 7th & + & -- & + & -- & + & -- & + & & & \\
\midrule
8 & 1st & + & + & + & + & + & + & + & + & & \\
& 2nd & + & + & + & + & -- & -- & -- & -- & & \\
& 3rd & + & + & 0 & -- & -- & 0 & + & + & & \\
& 4th & + & + & -- & -- & + & + & -- & -- & & \\
& 5th & + & -- & -- & + & + & -- & -- & + & & \\
& 6th & + & -- & 0 & + & -- & 0 & + & -- & & \\
& 7th & + & -- & + & -- & -- & + & -- & + & & \\
& 8th & + & -- & + & -- & + & -- & + & -- & & \\
\midrule
9 & 1st & + & + & + & + & + & + & + & + & + & \\
& 2nd & + & + & + & + & 0 & -- & -- & -- & -- & \\
& 3rd & + & + & + & -- & -- & -- & + & + & + & \\
& 4th & + & + & -- & -- & 0 & + & + & -- & -- & \\
& 5th & + & 0 & -- & 0 & + & 0 & -- & 0 & + & \\
& 6th & + & -- & -- & + & 0 & -- & + & + & -- & \\
& 7th & + & -- & + & + & -- & + & + & -- & + & \\
& 8th & + & -- & + & -- & 0 & + & -- & + & -- & \\
& 9th & + & -- & + & -- & + & -- & + & -- & + & \\
\bottomrule
\end{tabular}
\end{table}
\end{document}