Question

what is the difference between hardsphere and realistic potentials also give some examples?

Answer 1

Hard Sphere potentials are basically ideal (ignoring the minute variations) models which are used to study physical problems. These are approximate replicas which help us understand the actual model with simplicity. In going from the actual real potential to the approximate representation there is a trade off of the details which is done keeping in mind that the minute details (that have been ignored) do not affect our study (substantially). The basic characteristics that must be kept in mind while choosing an appropriate mode are:

1. The model reproduces the properties of interest as closely as possible to the realistic system.

2. The model can be used to study a variety of properties.

3. The model simplifies the calculations.

So we see there is a great deal of trade off which results in compensation compared to the real system. Same is the situation for hard sphere and realistic potential. For instance we model the atoms like hard spheres which works in a number of situations but there are limitations where the model breaks down because even though the atoms are like hard spheres but the boundary is not very rigid and we know this through our understanding of chemical bonds for example the covalent bonds where the atoms overlap. Had the atoms been really hard spheres there would not have been an overlap. So the realistic potential is not exactly a hard sphere. The difference (in general) arises microscopically. For instance macroscopically we can easily treat the atoms as hard spheres and we do so in let say the kinetic theory of gases, fluid dynamics etc. but microscopically the model breaks down because the trade off that we did between the actual (realistic) potential and hard spheres doesn't work. Here the actual or more accurate description of potential is required to deal with the system. This accuracy can be achieved starting with the hard sphere using the perturbation techniques as we do in quantum mechanics because they are easy do deal with and can be analytically solved exactly . Thus we can conclude "Hard spheres are good starting point for perturbative calculations of properties or systems of more realistic potentials".

Keyline: Hard spheres are simplest approximations of realistic potentials to start with and then the accuracy can be achieved by perturbing the hard spheres depending on the type od realistic potential