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How to plot the Free particle wave function

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Pouyan Msgn
Pouyan Msgn on 20 Apr 2021 at 16:33
Commented: Pouyan Msgn on 20 Apr 2021 at 17:23
Hello!
I have the function:
And a plot from my book is :
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
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 :
How can I get the correct plot?!

Accepted Answer

David Hill
David Hill on 20 Apr 2021 at 17:06
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);
  2 Comments
Pouyan Msgn
Pouyan Msgn on 20 Apr 2021 at 17:23
It worked for me in intervall -10 to 10! thank you

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