update

Author: mhjensen

doc/src/FuturePlans/bellfig.pdf

@@ -112,4 +112,155 @@
 
 \end{tikzpicture}
 
+
+
+\begin{tikzpicture}[scale=1.0, line cap=round, line join=round]
+
+% Axes (optional)
+%\draw[->] (-6,0) -- (6,0) node[right] {$x$};
+%\draw[->] (0,0) -- (0,5.5) node[above] {$E$};
+
+% Parameters
+\def\a{0.15}    % curvature
+\def\b{2.5}     % well separation
+\def\Emax{4.5}
+\def\R{0.13}
+
+% --- Smooth double-well potential ---
+% V(x) = a (x^2 - b^2)^2
+\draw[thick, domain=-4.2:4.2, samples=300]
+  plot (\x, {\a*(\x*\x-\b*\b)^2});
+
+% --- Energy levels (drawn locally in each well) ---
+\foreach \n/\E in {0/0.5,1/1.5,2/2.5,3/3.5}{
+  % Left well levels
+  \draw[dashed] (-4.0,\E) -- (-1.2,\E);
+  % Right well levels
+  \draw[dashed] ( 1.2,\E) -- ( 4.0,\E);
+}
+
+% Emphasize ground states
+\draw[very thick] (-4.0,0.5) -- (-1.2,0.5);
+\draw[very thick] ( 1.2,0.5) -- ( 4.0,0.5);
+
+% --- Particles in the ground states ---
+\filldraw[white, thick] (-2.5,0.5) circle (\R);
+\filldraw[white, thick] ( 2.5,0.5) circle (\R);
+
+% Optional labels
+\node[below] at (-2.5,0.3) {$n=0$};
+\node[below] at ( 2.5,0.3) {$n=0$};
+
+\end{tikzpicture}
+
+
+\clearpage
+
+
+\begin{tikzpicture}[scale=1.0, line cap=round, line join=round]
+
+% -----------------------
+% Parameters
+% -----------------------
+\def\a{0.15}     % curvature of the double well
+\def\b{2.5}      % separation of wells
+\def\R{0.13}     % particle radius
+
+% -----------------------
+% Smooth double-well potential
+% V(x) = a (x^2 - b^2)^2
+% -----------------------
+\draw[thick, domain=-4.2:4.2, samples=300]
+  plot (\x, {\a*(\x*\x-\b*\b)^2});
+
+% -----------------------
+% Energy levels En = n + 1/2 (ħω = 1 units)
+% -----------------------
+\foreach \n/\E in {0/0.5,1/1.5,2/2.5,3/3.5}{
+  % Left well levels
+  \draw[dashed] (-4.0,\E) -- (-1.2,\E);
+  % Right well levels
+  \draw[dashed] ( 1.2,\E) -- ( 4.0,\E);
+}
+
+% Emphasize ground states (n=0)
+\draw[very thick] (-4.0,0.5) -- (-1.2,0.5);
+\draw[very thick] ( 1.2,0.5) -- ( 4.0,0.5);
+
+% -----------------------
+% Particles in ground states
+% -----------------------
+% Left particle (spin up)
+\filldraw[white, thick] (-2.5,0.5) circle (\R);
+\draw[->, thick] (-2.5,0.55) -- (-2.5,0.95);
+\node[above] at (-2.5,0.95) {$\uparrow$};
+
+% Right particle (spin down)
+\filldraw[white, thick] ( 2.5,0.5) circle (\R);
+\draw[->, thick] ( 2.5,0.95) -- ( 2.5,0.55);
+\node[below] at ( 2.5,0.50) {$\downarrow$};
+
+% -----------------------
+% Optional labels
+% -----------------------
+\node[below] at (-2.5,0.30) {$n=0$};
+\node[below] at ( 2.5,0.30) {$n=0$};
+
+\end{tikzpicture}
+
+
+\begin{tikzpicture}[scale=1.0, line cap=round, line join=round]
+
+% -----------------------
+% Parameters
+% -----------------------
+\def\a{0.15}     % curvature of the double well
+\def\b{2.5}      % separation of wells
+\def\R{0.13}     % particle radius
+
+% -----------------------
+% Smooth double-well potential with softened outer edges
+% V(x) = a (x^2 - b^2)^2 * exp(-0.03 x^2)
+% -----------------------
+\draw[thick, domain=-4.2:4.2, samples=400]
+  plot (\x, {\a*(\x*\x-\b*\b)^2 * exp(-0.03*\x*\x)});
+
+% -----------------------
+% Energy levels En = n + 1/2  (ħω = 1 units)
+% -----------------------
+\foreach \n/\E in {0/0.5,1/1.5,2/2.5,3/3.5}{
+  % Left well levels
+  \draw[dashed] (-4.0,\E) -- (-1.2,\E);
+  % Right well levels
+  \draw[dashed] ( 1.2,\E) -- ( 4.0,\E);
+}
+
+% Emphasize ground states (n = 0)
+\draw[very thick] (-4.0,0.5) -- (-1.2,0.5);
+\draw[very thick] ( 1.2,0.5) -- ( 4.0,0.5);
+
+% -----------------------
+% Particles in ground states
+% -----------------------
+
+% Left particle (spin up)
+\filldraw[black, thick] (-2.5,0.5) circle (\R);
+\draw[->, very thick] (-2.5,0.55) -- (-2.5,1.45);
+%\node[above] at (-2.5,1.45) {$\uparrow$};
+
+% Right particle (spin down)
+\filldraw[black, thick] ( 2.5,0.5) circle (\R);
+\draw[->, very thick] ( 2.5,1.45) -- ( 2.5,0.55);
+%\node[below] at ( 2.5,0.45) {$\downarrow$};
+
+% -----------------------
+% Optional labels
+% -----------------------
+\node[below] at (-3.5,0.0) {$n=0$};
+\node[below] at ( 3.5,0.0) {$n=0$};
+
+\end{tikzpicture}
+
+
+
 \end{document}