text: Like all known forms of matter, liquids are fundamentally quantum mechanical. However, under standard conditions (near room temperature and pressure), much of the macroscopic behavior of liquids can be understood in terms of classical mechanics. The "classical picture" posits that the constituent molecules are discrete entities that interact through intermolecular forces according to Newton's laws of motion. As a result, their macroscopic properties can be described using classical statistical mechanics. While the intermolecular force law technically derives from quantum mechanics, it is usually understood as a model input to classical theory, obtained either from a fit to experimental data or from the classical limit of a quantum mechanical description. An illustrative, though highly simplified example is a collection of spherical molecules interacting through a Lennard-Jones potential.
  For the classical limit to apply, a necessary condition is that the thermal de Broglie wavelength, 
  is small compared with the length scale under consideration. Here,  is the Planck constant and  is the molecule's mass. Typical values of  are about 0.01-0.1 nanometers (Table 1). Hence, a high-resolution model of liquid structure at the nanoscale may require quantum mechanical considerations. A notable example is hydrogen bonding in associated liquids like water, where, due to the small mass of the proton, inherently quantum effects such as zero-point motion and tunneling are important.
  For a liquid to behave classically at the macroscopic level,  must be small compared with the average distance  
  between molecules. That is, 
  Representative values of this ratio for a few liquids are given in Table 1. The conclusion is that quantum effects are important for liquids at low temperatures and with small molecular mass. For dynamic processes, there is an additional timescale constraint:
  where  is the timescale of the process under consideration. For room-temperature liquids, the right-hand side is about 10 seconds, which generally means that time-dependent processes involving translational motion can be described classically.
  At extremely low temperatures, even the macroscopic behavior of certain liquids deviates from classical mechanics. Notable examples are hydrogen and helium. Due to their low temperature and mass, such liquids have a thermal de Broglie wavelength comparable to the average distance between molecules.