Superconductivity

One quantum mechanical effect that shows itself on the macroscopic scale is superconductivity. Cooper-paired conduction electrons in superconductors have total spin zero, that is, their paired spins are opposite, even though their spatial separation can be enormous centimeters to meters, for example because they have opposite momenta. These pairs can act like bosons of spin zero, which obey Bose-Einstein statistics. Any number of bosons can be in the same quantum state, that is, have the same four-momentum (e.g., defined by the energy and three-momentum) and spin. Therefore, all bosons in the same collective superconducting state have exactly the same energy. Yet this boson collective state in a superconductor has a small energy width. Any thoughts about the cause of this energy width?

Answer

The paired electrons in superconductors that are in the superconducting state show Bose-Einstein condensation to a single macro state. There is some small energy width to this macro state because the pairs are composed of spin 1/2 particles, and they are showing remnant Fermi-Dirac behavior: no two identical fermions can ever be in the same state as defined by their four momenta and spins no matter how they behave collectively.