Learn about the 5 most common types of semiclassical physics approximations used to study quantum systems. Understand their limitations and benefits.

# 5 Most Common Types of Semiclassical Physics Approximations

Semiclassical physics approximations are methods of calculating the behavior of quantum systems using classical mechanics. These approximations are used when the quantum mechanical calculations are too difficult or time-consuming to perform. In this article, we will discuss the five most common types of semiclassical physics approximations.

## 1. WKB Approximation

The WKB (Wentzel-Kramers-Brillouin) approximation is a semiclassical method of finding approximate solutions to the SchrĂ¶dinger equation. This method is particularly useful for finding solutions to the equation in regions where the potential energy is greater than the kinetic energy. The WKB approximation assumes that the wave function varies slowly over short distances and rapidly over long distances. This approximation is useful in calculating tunneling probabilities and in the study of energy levels in atoms.

## 2. Born-Oppenheimer Approximation

The Born-Oppenheimer approximation is a semiclassical method that separates the motion of the atomic nuclei and electrons in a molecule. This approximation assumes that the atomic nuclei move much more slowly than the electrons, and therefore, the electronic motion can be calculated first, and the nuclear motion can be calculated second. This approximation is useful in calculating molecular energy levels and in the study of chemical reactions.

## 3. Thomas-Fermi Approximation

The Thomas-Fermi approximation is a semiclassical method of calculating the electronic density in a many-electron system. This approximation assumes that the