Charge density many of them in a macroscopic volume (there are about 10 conduction electrons in a cubic centimeter of copper) the continuous approximation is very accurate when applied to macroscopic volumes, and even microscopic volumes above the nanometer level. At atomic scales, due to the uncertainty principle of quantum mechanics, a charged particle does not "have" a precise position but is represented by a probability distribution, so the charge of an individual particle is not concentrated at a point but is 'smeared out' in space and acts like a true continuous charge distribution. This is the meaning of 'charge distribution' and
Particle in a ring in that case are identical to the energy eigenfunctions of the particle on a ring. The statement that any wavefunction for the particle on a ring can be written as a superposition of energy eigenfunctions is exactly identical to the Fourier theorem about the development of any periodic function in a Fourier series. This simple model can be used to find approximate energy levels of some ring molecules, such as benzene. In organic chemistry, aromatic compounds contain atomic rings, such as benzene rings (the Kekulé structure) consisting of five or six, usually carbon, atoms. So does the surface of "buckyballs"