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ziezi
Posts: 3
Joined: Mon Sep 17, 2018 5:02 pm

Strangely looking trigonometric function plots?

Postby ziezi » Mon Sep 17, 2018 5:18 pm

I'm trying to plot simple trigonometric functions,sin(x), sin^{2}(x), with the following code:

  1. \documentclass[a4paper]{article}
  2. \usepackage{pgfplots}
  3. \pgfplotsset{compat=1.14}
  4.  
  5. \begin{document}
  6. \begin{tabular}{@{}c@{}}
  7. \begin{tikzpicture}
  8. \begin{axis}[
  9. width = \axisdefaultwidth,
  10. height = 0.3\textheight,
  11. xlabel = $x$,
  12. ylabel = $\psi(x)$,
  13. title = {Wavefunction in periodic potential.},
  14. xmin = 0, xmax = 10,
  15. ymin = -1.2, ymax = 1.2,
  16. xtick = {0, 2, ..., 10},
  17. xticklabels = {$0$, $a$, $2a$, $3a$, $4a$, $5a$},
  18. ]
  19.  
  20. \addplot [color = red, domain = 0 : 10, smooth] plot {cos(deg(\x*pi))}
  21. node [pos = 0.3, above right] {$cos(x)$};
  22. \addplot [color = blue, domain = 0 : 10, smooth] plot {sin(deg(\x*pi))}
  23. node [pos = 0.9, above left] {$sin(x)$};
  24.  
  25. \addlegendentry{$\psi_{+}(x)$};
  26. \addlegendentry{$\psi_{-}(x)$};
  27. \end{axis}
  28. \end{tikzpicture}
  29. \\
  30. \begin{tikzpicture}
  31. \begin{axis}[
  32. width = \axisdefaultwidth,
  33. height = 0.3\textheight,
  34. xlabel = $x$,
  35. ylabel = $\rho(x)$,
  36. title = {Probability density in periodic potential.},
  37. xmin = 0, xmax = 10,
  38. ymin = 0, ymax = 2.5,
  39. xtick = {0, 2, ...,10},
  40. xticklabels = {$0$, $a$, $2a$, $3a$, $4a$, $5a$},
  41. ]
  42.  
  43. \addplot [color = red, domain = 0 : 10, smooth] plot {2*cos(deg(\x*pi))^2}
  44. node [pos= 0.3, above right] {$cos^{2}(x)$};
  45. \addplot [color = blue, domain = 0 : 10, smooth] plot {2*sin(deg(\x*pi))^2}
  46. node [pos = 0.9, above left] {$sin^{2}(x)$};
  47.  
  48. \addlegendentry{$\rho_{+}(x)$};
  49. \addlegendentry{$\rho_{-}(x)$};
  50. \end{axis}
  51. \end{tikzpicture}
  52. \end{tabular}
  53. \end{document}


and I get strange results. The plots are way off of what they should be, i.e. the $sin(x)$ and $cos(x)$ are not smooth and drifting on the y-axis. The $sin^{2}(x)$ and $cos^{2}(x)$ are horrendous.

The intended result is to plot 5 peaks where the cos(x) has its maximums over a, 2a, 3a, etc. similar to the grey plots.

Why are the plots like this? What am I doing wrong?
Attachments
goal.JPG
goal.JPG (69.62 KiB) Viewed 320 times
current.JPG
current.JPG (42.16 KiB) Viewed 325 times
Last edited by ziezi on Mon Sep 17, 2018 5:39 pm, edited 1 time in total.

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Stefan Kottwitz
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Posts: 9192
Joined: Mon Mar 10, 2008 9:44 pm

Postby Stefan Kottwitz » Mon Sep 17, 2018 5:30 pm

Perhaps remove the factor pi in the argument:


  1. \addplot [color = red, domain = 0 : 10, smooth] plot {cos(deg(x))}
  2. node [pos = 0.3, above right] {$cos(x)$};
  3. \addplot [color = blue, domain = 0 : 10, smooth] plot {sin(deg(x))}
  4. node [pos = 0.9, above left] {$sin(x)$};
  5.  
  6. ...
  7.  
  8. \addplot [color = red, domain = 0 : 10, smooth] plot {2*cos(deg(x))^2}
  9. node [pos= 0.3, above right] {$cos^{2}(x)$};
  10. \addplot [color = blue, domain = 0 : 10, smooth] plot {2*sin(deg(x))^2}
  11. node [pos = 0.9, above left] {$sin^{2}(x)$};


Stefan
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Stefan Kottwitz
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Posts: 9192
Joined: Mon Mar 10, 2008 9:44 pm

Postby Stefan Kottwitz » Mon Sep 17, 2018 5:32 pm

By the way, math operators are commonly written upright, not italic, there are macros for it:

  1. node [pos = 0.3, above right] {$\cos(x)$};
  2. node [pos = 0.9, above left] {$\sin(x)$};


Stefan
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ziezi
Posts: 3
Joined: Mon Sep 17, 2018 5:02 pm

Postby ziezi » Mon Sep 17, 2018 5:45 pm

Thank you for the fast response!

You are right, removing pi from the argument makes things better, however, I don't know how to plot specific number of maximums, matched to specific points on the x-axis, corresponding with the maximums of the other plot below.

I've updated the question and included additional information.

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Stefan Kottwitz
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Posts: 9192
Joined: Mon Mar 10, 2008 9:44 pm

Postby Stefan Kottwitz » Mon Sep 17, 2018 7:44 pm

Try this, notice the xticks settings:

  1. \documentclass[a4paper]{article}
  2. \usepackage{pgfplots}
  3. \pgfplotsset{compat=1.14}
  4. \pgfmathsetmacro{\PI}{pi}
  5. \begin{document}
  6. \begin{tikzpicture}
  7. \begin{axis}[
  8. width = \axisdefaultwidth,
  9. height = 0.3\textheight,
  10. xlabel = $x$,
  11. ylabel = $\rho(x)$,
  12. title = {Probability density in periodic potential.},
  13. xmin = 0, xmax = 16,
  14. ymin = 0, ymax = 2.5,
  15. scaled x ticks={real:\PI},
  16. xtick scale label code/.code={},
  17. xtick distance=pi,
  18. xticklabels = {,,$a$, $2a$, $3a$, $4a$, $5a$}
  19. ]
  20. \addplot [color = red, domain = 0 : 16, samples = 150, smooth] plot {2*cos(deg(x))^2}
  21. node [pos= 0.3, above right] {$\cos^{2}(x)$};
  22. \addlegendentry{$\rho_{+}(x)$};
  23. \addlegendentry{$\rho_{-}(x)$};
  24. \end{axis}
  25. \end{tikzpicture}
  26. \end{document}


cos-plot.png
cos-plot.png (23.12 KiB) Viewed 309 times


Stefan
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ziezi
Posts: 3
Joined: Mon Sep 17, 2018 5:02 pm

Postby ziezi » Mon Sep 17, 2018 10:25 pm

Thanks again for the suggestion! It worked great!

I hope that by clicking accept on the last answer I've closed/completed the question.

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Stefan Kottwitz
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Posts: 9192
Joined: Mon Mar 10, 2008 9:44 pm

Postby Stefan Kottwitz » Mon Sep 17, 2018 11:30 pm

Yes, that's perfect. Clicking the checkmark at that post that was the solution, marks the whole topic as solved (so supporters see it) and makes that solution the hyperlink when one clicks the checkmark at the top, so google searchers can jump to the solution.

Stefan
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