How to plot rectangular potential in matlab

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 ?

Answer 1

[Star Strider]

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.

[Pouyan Msgn]

Yes but the step function; U has the value 5e-19; how I can plot that ?

[Star Strider]

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.

[Pouyan Msgn]

Thank you ^_^

[Star Strider]

My pleasure.

If my Answer helped you solve your problem, please Accept it!

[Pouyan Msgn]

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]

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]

Thanks and I clicked on accepted

[Star Strider]

As always, my pleasure!