Hi Khaled,
I understand that you want to plot the probability density quantum harmonic oscillator.
Assuming the oscillator is a 1D oscillator, you can define the wave function for harmonic oscillator using the equation 
as: “psi = (m * omega / pi)^(1/4) * exp(-0.5 * m * omega * x.^2);”
This is the wave function for the ground state of the harmonic oscillator. To find the above equation’s probability density, you can use “abs(psi).^2”. Refer the example code below for better understanding:
% Define the parameters of the harmonic oscillator
m = 1; % Mass
omega = 1; % Angular frequency
% Define the range of x values
x = linspace(-5, 5, 1000);
% Calculate the wave function
psi = (m * omega / pi)^(1/4) * exp(-0.5 * m * omega * x.^2);
% Calculate the probability density
probability_density = abs(psi).^2;
% Plot the probability density
plot(x, probability_density, 'LineWidth', 2);
xlabel('Position (x)');
ylabel('Probability Density');
title('Probability Density of Quantum Harmonic Oscillator');
grid on;
Feel free to adjust the range of x values or modify the parameters (“m” and “omega”) to explore different scenarios.
Hope it helps!
Regards,
Ayush
