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Actually wanted to draw and plot Optical and acoustic branch but don't know it what's the command to draw a function like this ? enter image description here

Thanks for the help

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    I wouldl guess that the math refers only to the intersections with the axes, (0-\pi/a ?). You really don't have enough information here to do anything. I would overlay some graph paper and start recording points, then graph using smooth. Jun 15 '19 at 12:53
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pgfplots can produce such plots.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[declare function={%
 omegaplus(\k,\K,\a,\mone,\mtwo)=sqrt(\K*(1/\mone+1/\mtwo)+
 \K*sqrt((1/\mone+1/\mtwo)^2-4*pow(sin(\k*\a/2),2)/(\mone*\mtwo)));
 omegaminus(\k,\K,\a,\mone,\mtwo)=sqrt(\K*(1/\mone+1/\mtwo)-
 \K*sqrt((1/\mone+1/\mtwo)^2-4*pow(sin(\k*\a/2),2)/(\mone*\mtwo)));}]
  \begin{axis}[axis x line=bottom,axis y line=middle,trig format=rad,
    xlabel={$k$},xtick=\empty,ytick=\empty,ymax=2,xmax=3.5,clip=false,
    xticklabels={},yticklabels={},trig format=rad]
    \addplot[color=red,domain=0:pi,smooth,samples=51] {omegaplus(x,1,1,1,2)}
    node[pos=0,left,black]{$\displaystyle2C\left(\frac{1}{m_1}+\frac{1}{m_2}\right)^{1/2}$}
    node[pos=1,right,black]{$\displaystyle\left(\frac{2C}{m_1}\right)^{1/2}$}
    node[midway,above,sloped,font=\sffamily]{optical branch};
    \addplot[color=blue,domain=0:pi,smooth,samples=51] {omegaminus(x,1,1,1,2)}
    node[pos=1,right,black]{$\displaystyle\left(\frac{2C}{m_2}\right)^{1/2}$}
    node[midway,above,sloped,font=\sffamily]{acoustic branch};
   \draw[thick] (pi,0)  -- (pi,2);
  \end{axis}
\end{tikzpicture}
\end{document}

enter image description here

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  • Thanks a lot , could you explain what you've done here by declaring the function and how do you put "acoustic branch" and "optical branch" in exact proper position.
    – Quintis
    Jun 16 '19 at 5:55
  • @Quintis (I see this comment only now, sometimes comments get swallowed by the system.) All I did was to punch in the dispersion relations for phonons, which can be found e.g. here. And then you can position stuff with pos=<f> where f=0 is the start and f=1 the end of the plot.
    – user121799
    Jun 19 '19 at 21:24

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