How to plot rectangular potential in matlab

2018 11 8
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更新时间：2018 11 8
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I will try to plot something like this :
Observ that this is a rectangular potential barrier, the dashed line is the classical result of the potential U and the blue line is the quantum mechanics. The tunneling regime takes the place at intersection of the dashed line and the blue line; and the tops of the blue line is called the resonance which I have to show. My attempt is
clc
clear all
m=9.11 * 10^(-31);
U=5e-19;
E=0e-19:0.001e-19:12e-19;
a=3e-9;
h=1.36e-34;
k=sqrt(2*m.*(U-E));
k2=k/h;
c=(U^2)*(sinh(0.5*a*k2).^2)./(4*E.*(U-E));
T=1./(1+c);
plot(E,T)
But how can I get a plot like this ?

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Star Strider
Star Strider 2018-11-8

1 个投票

Your code appears to be correct. If you want the labels, try this:
m=9.11E-31;
U=5e-19;
E=0e-19:0.001e-19:12e-19;
a=3e-9;
h=1.36e-34;
k=sqrt(2*m.*(U-E));
k2=k/h;
c=(U^2)*(sinh(0.5*a*k2).^2)./(4*E.*(U-E));
T=1./(1+c);
[respks, locs] = findpeaks(T);
figure
plot(E,T)
hold on
plot([0.5 0.5]*1E-18, ylim, '--r')
hold off
text(E(locs+275), respks*0.99, compose('\\bf{\\leftarrow res %d}', 1:3), 'HorizontalAlignment','left', 'VerticalAlignment','top', 'Rotation', -75)
text(0.5E-18, 0.1, sprintf('\\bftunneling \\rightarrow'), 'HorizontalAlignment','right')
Experiment to get the result you want.

8 个评论
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Pouyan Msgn
Pouyan Msgn 2018-11-8
Yes but the step function; U has the value 5e-19; how I can plot that ?
Star Strider
Star Strider 2018-11-8
Plot it as a continuous function:
m=9.11E-31;
U=5e-19;
E=0e-19:0.001e-19:12e-19;
a=3e-9;
h=1.36e-34;
k=sqrt(2*m.*(U-E));
k2=k/h;
c=(U^2)*(sinh(0.5*a*k2).^2)./(4*E.*(U-E));
T=1./(1+c);
stp = @(x) x >= 0;
[respks, locs] = findpeaks(T);
figure
plot(E,T)
hold on
plot(E, stp(E-U), '--r')
hold off
text(E(locs+275), respks*0.99, compose('\\bf{\\leftarrow res %d}', 1:3), 'HorizontalAlignment','left', 'VerticalAlignment','top', 'Rotation', -75)
text(0.5E-18, 0.1, sprintf('\\bftunneling \\rightarrow'), 'HorizontalAlignment','right')
This is essentially the same as before, changed to include the addition of the ‘stp’ anonymous function, and the plot call that plots it as a step function.
Star Strider
Star Strider 2018-11-8
My pleasure.
If my Answer helped you solve your problem, please Accept it!
Pouyan Msgn
Pouyan Msgn 2018-11-8
But one thing I get this error when I run it : Undefined function 'compose' for input arguments of type 'char'.
Error in Q3a (line 21) text(E(locs+275), respks*0.99, compose('\\bf{\\leftarrow res %d}', 1:3), 'HorizontalAlignment','left', 'VerticalAlignment','top', 'Rotation', -75)
Star Strider
Star Strider 2018-11-8
编辑：Star Strider 2018-11-8
The compose function was introduced in R2016b.
This should work:
text(E(locs+275), respks*0.99, sprintfc('\\bf{\\leftarrow res %d}', 1:3), 'HorizontalAlignment','left', 'VerticalAlignment','top', 'Rotation', -75)
Note — The sprintfc function is officially undocumented.
Pouyan Msgn
Pouyan Msgn 2018-11-8
Thanks and I clicked on accepted

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