Numerically Calculating the Infinite Potential Well?

For my quantum mechanics class, we've been asked to write a program which find energy levels for potential energy wells of different shapes. I'm starting with a simple infinite potential well stretching from -10 to 10 angstroms and manually entering the energy just to debug the method we're expected to use, but I can't seem to get it to work. We're supposed to have the program loop through these three equations to find the value of the wavefunction: http://i45.tinypic.com/u9bvn.gif

My wavefunction should look like this when I put in the second energy level (0.376 eV), with it staying near zero for a while before the program goes too far into the infinite potential: http://i46.tinypic.com/2m2c9cw.gif

Instead, my wavefunction hits zero-ish and immediately skyrockets to infinity, which is supposed to show that the energy value is incorrect. http://i50.tinypic.com/jv6glt.gif

What is wrong with my code? Here is what I have:

%Symmetric_Well.m
%This program is an attempt to find the energy values for a wavefunction in
%a symmetric well which stretches from -10 to 10.

clear;

%Define variables
step = 0.1;
value = 1:101;
slope = 1:101;
curve = 1:101;
x = 1:101;
value(1) = 1;
slope(1) = 0;
beta = 0.26246;

%Zero the arrays
for j=1:101;
    value(j)=0;
    slope(j)=0;
    curve(j)=0;
    x(j)=0;
end

%Initial conditions
value(1) = 0;
slope(1)= 1;
x(1)=0.1;

%Receive guess from user
Energy = input('Please enter an energy value in electron volts.');

%Set up loop
for i=2:102;
    x(i) = i*step;
    k = i-1;

      %Draw potential
      if abs(x(i))<10, V=0;
      else V=100000000000;
      end

      curve(i) = beta*(V-Energy)*value(k);
      slope(i) = slope(k)+curve(k)*step;
      value(i) = value(k)+slope(k)*step+(curve(k)*step^2)/2;
  end

%Make a plot
plot(x, value);
axis([0 15 -5 5]);
xlabel('Distance in angstroms');
ylabel('Energy in electron volts');

Answer 1

[Abdul Wahab]

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Numerically Calculating the Infinite Potential Well? 56 views (last 30 days) Rachel Rachel on 23 Feb 2013 ⋮ For my quantum mechanics class, we've been asked to write a program which find energy levels for potential energy wells of different shapes. I'm starting with a simple infinite potential well stretching from -10 to 10 angstroms and manually entering the energy just to debug the method we're expected to use, but I can't seem to get it to work. We're supposed to have the program loop through these three equations to find the value of the wavefunction: http://i45.tinypic.com/u9bvn.gif My wavefunction should look like this when I put in the second energy level (0.376 eV), with it staying near zero for a while before the program goes too far into the infinite potential: http://i46.tinypic.com/2m2c9cw.gif Instead, my wavefunction hits zero-ish and immediately skyrockets to infinity, which is supposed to show that the energy value is incorrect. http://i50.tinypic.com/jv6glt.gif What is wrong with my code? Here is what I have: %Symmetric_Well.m %This program is an attempt to find the energy values for a wavefunction in %a symmetric well which stretches from -10 to 10. clear; %Define variables step = 0.1; value = 1:101; slope = 1:101; curve = 1:101; x = 1:101; value(1) = 1; slope(1) = 0; beta = 0.26246; %Zero the arrays for j=1:101; value(j)=0; slope(j)=0; curve(j)=0; x(j)=0; end %Initial conditions value(1) = 0; slope(1)= 1; x(1)=0.1; %Receive guess from user Energy = input('Please enter an energy value in electron volts.'); %Set up loop for i=2:102; x(i) = i*step; k = i-1; %Draw potential if abs(x(i))<10, V=0; else V=100000000000; end curve(i) = beta*(V-Energy)*value(k); slope(i) = slope(k)+curve(k)*step; value(i) = value(k)+slope(k)*step+(curve(k)*step^2)/2; end %Make a plot plot(x, value); axis([0 15 -5 5]); xlabel('Distance in angstroms'); ylabel('Energy in electron volts')

Answer 2

[Abdul Wahab]

step = 0.1; value = 1:101; slope = 1:101; curve = 1:101; x = 1:101; value(1) = 1; slope(1) = 0; beta = 0.26246; %Zero the arrays for j=1:101; value(j)=0; slope(j)=0; curve(j)=0; x(j)=0; end