Quantum Mechanical Systems Simulator

This program simulates four different quantum mechanical systems called the infinite well, the harmonic oscilator, the step, and the barrier. The difference among them is the potential distribution along the X axis. These are the most common potentials when studying the Schrodinger equation for the wave function that reads:

The first system is the infinite well, its potential is zero when |x|<L/2, but when |x|>L/2, then the value of the potential is infinite. It is easy to deduce the eigenstate functions of this system. Indeed the program draws the wave function analytically. The following image shows some of the wave functions that the program can draw. It is interesting to mention that the program can simulte correctly the Bohr's correspondence principle for high values of n (60 or higher). As we can see in the following image, the probability density is almost the same for any value of x.

The next system is the potential step. Here the potential seems a single step of a normal stair due to the fact that its value is zero for x<0, but changes to Vo for positive values of x. The program is able to draw the wave function associated to the energy of the particle analytically. As we can see using the program, the wave function is continuous and soft.

The potential barrier is very similar to the potential step. In this case, the potential turns to zero again for positive values of x that are higher than L(barrier size). This system has three zones  to study, and as expected, the wave function is continuous and soft in all the zones. Moreover, we can see that the wave function is completely different when we study either incoming particles with high energys(E>Vo) or particles with lower energys(E<Vo).

To sum up, we can study the harmonic oscilator, whose wave function is fairly complex due to the fact that its values must be calculated using numerical methots. In this case, the program uses the finite differences method. This numerical method doesn't give exact solutions so the program is not reliable for high values of n.

When we launch the program, we will see something like this:

To download it, please, visit the downloads section.