Particle in a Central Potential

Most physical problems take place in three-dimensional space. We will study the stationary Schrödinger equation for a particle subjected to a potential in this space. The problem is simplified if the potential is spherically symmetric.spherical symmetry This type of potential is called a central potential.Central potential In this case, the ( 4.4.6 ) form of the stationary Schrödinger equation is too general, as a central potential does not depend on the direction of the vector $$\textbf{r}$$ . The interest in these potentials comes from the fact that the fundamental interactions of nature (Sect. 1.2.2 ) are rotationally invariant.Rotational invariance The interaction between two particles does not depend on the orientation of the system formed by these particles. It has the same intensity in all directions of space. It is proven in Sect. 10.5 that the study of a system of two particles comes down to the problem that we study in this chapter. The notion of orbital angular momentum detailed in Chap. 8 plays an essential role for the solution of the stationary Schrödinger equation with a central potential.