pgfplots How to add marker defined by x value and existing function?

Question

This is my first time using tikz/pgfplots; I'm not even sure I understand the difference between tiki and pgfplots. Please forgive my ignorance.

I have a plot defined as:

\begin{tikzpicture}
\begin{axis}[
  ticks = none,
  axis lines = center,
  xlabel = energy,
  ylabel = cross section,
  xlabel style = {below},
  ylabel style = {left,rotate=90},
  xmin = 0.0,
  xmax = 5,
  ymin = 0.0,
  ymax = 2.0,
]
\addplot[
  blue,
  samples=200,
] {1/sqrt(x)};
\end{axis}
\end{tikzpicture}

Now I want to add some points (markers) on the curve (defined by 1/sqrt(x)) at a few points specified by the x-value (0.5, 1.25, 1.5, 1.75, 2.20). I could determine the y-value for each x-value, but I figured there was someway for LaTeX to determine what the y-value was.

I'd like to add these points individually as I'll be animating this in Beamer at a later date.

---

On a different note, how can I center the axes labels at the center of the axes instead of the end?

Answer 1

You can use samples at key

\begin{tikzpicture}
\begin{axis}[
  ticks=none,
  axis x line=bottom,
  axis y line=left,
  xlabel = energy,
  ylabel = cross section,
  xmin = 0.0,
  xmax = 5,
  ymin = 0.0,
  ymax = 2.0,
]
\addplot[blue,samples=200]{1/sqrt(x)};
\addplot[only marks,samples at={0.5, 1.25, 1.5, 1.75, 2.20}]{1/sqrt(x)};
\end{axis}
\end{tikzpicture}

Answer 2

\documentclass[border=2mm,tikz]{standalone}
\usepackage{pgfplots}
\begin{document}
\xdef\Lst{}
\foreach \X in {0.5, 1.25, 1.5, 1.75, 2.20}
{\xdef\Lst{\Lst (\X,{1/sqrt(\X)})}}
\typeout{\Lst}
\begin{tikzpicture}
\begin{axis}[
  ticks = none,
  axis lines = center,
  xlabel = energy,
  ylabel = cross section,
  xlabel style = {below,anchor=north east},
  ylabel style = {above,rotate=90,anchor=south east},
  xmin = 0.0,
  xmax = 5,
  ymin = 0.0,
  ymax = 2.0,
]
\addplot[
  blue,
  samples=200,
] {1/sqrt(x)};
\addplot[only marks,
  red] coordinates \Lst;
\end{axis}
\end{tikzpicture}
\end{document}