Hello! I am trying to write a program that solves the Schrodinger Equation for a particle in an infinite square well. I did a lot of research regarding the methods that could be used to accomplish this. I am writing this program in Matlab. The method I am using is called the Shooting Method. In my code below, when I plot psi vs. x_negative, I do not get a wave function that looks like what we expect. I am not sure where I am going wrong with this. I also don't know how much details I should include in this thread. Please, ask me for more information if needed. I have also attached picture of the textbook I am using for my logic. It is from the Computational Physics textbook by N. Giordano. Thank you very much for your help!(adsbygoogle = window.adsbygoogle || []).push({});

<Moderator's note: please use code tags>Code (Matlab M):

clear;

clc;

%declaring variables

psi = zeros(1,200); %Wave function

dx = 0.01; %x steps

V = 1000; %potential outside the well

e = 3; %initial guess energy

de = -.6; %energy step-size.

%boundry conditions

psi(1) = 1;

psi(2) = 1;

last_diverge = 0; %keeping track of the curvature of the wave function

flag = 't'; %variable to control the while loop below

while flag == 't'

%this for loop needs to be nested in another loop

for k = 2:length(psi)-1

%defining the potential funtion of the well

if abs(k*dx) <= 1

potential = 0;

else

potential = V;

end

psi(k+1) = 2*psi(k) - psi(k-1) - 2*(e - potential)*(dx^2)*psi(k);

%if psi exceeds the maximum magnitude, then exit the loop

if psi(k+1) > 2

break;

end

end

%plotting the left side of the wave function

f = 1;

for n = -k:0

x_negative(f) = n*dx;

f = f + 1;

end

%asking the user if they want to estimate more

flag = input('Enter (t) if you would like to continue finding the solution: ','s');

%updating the curvature of the wave function

if psi(k+1) > 0

diverge = 1;

else

diverge = -1;

end

if diverge * last_diverge < 0

de = -(de/2);

end

e = e + de;

last_diverge = diverge;

end

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# "Shooting Method" for simulating a Particle in an Infinite Square Well

Tags:

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**