Cold & quantum

One of the most fascinating, and paradigm-shifting, aspects of quantum mechanics is the notion that even massive particles have wave-like properties. Encapsulated in the famous relationship between momentum (p), wavelength (\lambda), and Planck's constant, the de Broglie wavelength can be thought of as the typical extent of a particle (or, more precisely, of its wavefunction).

When particles are colder, their momentum (which is proportional to speed) is reduced, and the de Broglie wavelength grows. For dense systems, sufficiently low temperatures result in a wavelength that exceeds the inter-particle spacing. At this point, the individual particles start to lose their identities, and many-body effects begin to emerge.

Let's consider a simple model -- the infinite square well -- and study the nature of some wavefunctions at different temperatures: