Answer to Question #157541 in Quantum Mechanics for Max

Question

What is virial theorem

Answer 1

The virial theorem is a relation that connects the average kinetic energy of a system of particles with the forces acting in it. The virial G for the set of N point particles in mechanics is defined as:

$G=\sum{\overrightarrow{p}_k\cdot\overrightarrow{r}_k}$ ,

where $\overrightarrow{p}_k$ and $\overrightarrow{r}$ are the spatial vectors of momentum coordinates and coordinates for the k-th particle. For a stable system bound by potential forces, the virial theorem is

$<T>=-\frac{1}{2}\sum{\overrightarrow{F}_k\cdot\overrightarrow{r}_k}$

where $<T>$ is the average total kinetic energy; $\overrightarrow{F}_k$ is the force acting on the k-th particle.