As mentioned in the introductory video, this section is supposed to show you that we can apply our methods even to quantum physics where we solve the stationary Schrdinger equation. The only difficulty is that we have to solve this differential equation for the energy and the wave function at the same time. A valid method, to solve such an equation is called 'shooting method'. This procedure is explained and programmed in the videos of this section.

The origin of the Schrdinger equation is difficult to explain in short. For this course, we will just 'accept' this equation and will only solve it. For more background information, you may consider my udemy course about quantum physics. There, you can explore more mathematical details of this equation. Here is a teaser:


Motivation of the Schrdinger equation based on the particle/wave character of electrons

(right-click and open in new tab for better resolution)

Derivation of the stationary Schrdinger equation for time-independent potentials


We must solve this equation for the eigenenergies E and the wave functions phi. The result will strongly depend on the considered potential V(r) that characterizes the physical system. In the following we will consider two examples for such potentials: