How to plot the Free particle wave function
14 views (last 30 days)
Show older comments
Hello!
I have the function:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/590647/image.png)
And a plot from my book is :
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/590652/image.jpeg)
As you see in the picture,
as a function of x/a is ploted. I tried to program this in Matlab with optional parameters but I dont get the correct picture
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/590657/image.png)
My code is:
clc
clear all
a=10;
k=-100:1:100;
c1=pi*sqrt(2*a);
h=(6.626/(2*pi))*10^-34;
m=9.11*10^-31;
N=length(k);
xb=60;
h=2*xb/(N-1);
x=-xb:h:xb;
t=m*a*a/h;
V=zeros(N,1);
S=0;
f=@(k,x)(1/c1)*((sin(k*a)./k)*exp(i*(k.*x-(h/(2*m))*t.*(k.^2))));
for i=1:length(k)-1
c=f(k(i),x(i))+f(k(i+1),x(i));
S=S+c*0.5;
V(i)=S;
end
Ps=abs(V).^2;
plot(x/a,a*Ps)
grid on
The plot is :
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/590662/image.jpeg)
How can I get the correct plot?!
0 Comments
Accepted Answer
David Hill
on 20 Apr 2021
a=10;
c1=pi*sqrt(2*a);
h=(6.626/(2*pi))*10^-34;
m=9.11*10^-31;
X=-60:.1:60;
t=m*a^2/h;
V=zeros(1,201);
for j=1:length(X)
f=@(k)((sin(k*a)./k).*exp(1i*(k.*X(j)-(h/(2*m))*t.*(k.^2))));
V(j)=integral(f,-100,100);
end
plot(X/a,a*abs(V).^2);
More Answers (0)
See Also
Categories
Find more on Bartlett in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!