Central Potential (also known as
spherically symmetric potential )

Introduction
Central Potential problems are associated with a generic class of three-dimensional physical
systems. For a general two or three-dimensional potential, without any symmetry, the
solutions of the Schrodinger equation are often inaccessible.
• These are the systems that have a central potential, i.e. a potential energy that depends
only on the distance r from the origin
Example: Coulomb potential between electrically charged particles:
Hydrogen atom; where there is a proton inside nucleus and an electron outside nucleus.
Why we use spherical/cylindrical/Cartesian coordinate
system ?
Calculations become more easier if one use a coordinate system that look like the problem.
spherical coordinates are more helpful in dealing with the problems with spherical
symmetry, such as the gravity of a planet or a hydrogen atom. Similarly for cylindrical
symmetry, as in case of magnetic field of a wire, cylindrical coordinates will be more useful.

Separation of Variables

Magnetic Quantum Number

Principal Quantum
Number
Orbital Quantum
Number

Using
taking common
2m/hbar2