Currently, it is not well understood how high the energy of an eigenstate of the hard sphere gas must be in order for it to obey the ETH. A rough criterion is that the average thermal wavelength of each particle be sufficiently smaller than the radius of the hard sphere particles, so that the system can probe the features which result in chaos classically (namely, the fact that the particles have a finite size ). However, it is conceivable that this condition may be able to be relaxed, and perhaps in the thermodynamic limit, energy eigenstates of arbitrarily low energies will satisfy the ETH (aside from the ground state itself, which is required to have certain special properties, for example, the lack of any nodes ).