Hard spheres potential

Hard spheres are widely used as model particles in the statistical mechanical theory, defined as impenetrable spheres that cannot overlap in space, which mimics extremely strong repulsion that atoms and molecules experience at very close distances.

Conditions:

1. Spheres are identical.

Links:

1. Wikipedia.

potential

potential_energy of the configuration.

Symbol:

U

Latex:

\(U\)

Dimension:

energy

distance

euclidean_distance between the centers of the particles.

Symbol:

r

Latex:

\(r\)

Dimension:

length

sphere_diameter

diameter of the spheres.

Symbol:

sigma

Latex:

\(\sigma\)

Dimension:

length

law

U = Piecewise((Infinity, r <= sigma), (0, r > sigma))

Latex:

\[\begin{split}U = \begin{cases} \infty & r \le \sigma \\ 0 & r > \sigma \end{cases}\end{split}\]