# One dimensional quantum wire

1. Dec 28, 2008

### lion8172

I have seen, in several places, derivations of a formula for the current flow in a 1d quantum wire connected to electron reservoirs at its respective terminals. All of these derivations at some point invoke the formula for the number of states per unit volume of a 1d quantum "box,"
n(k) dk = (2 /pi) dk, but note, at the same time, that the conduction electrons are only confined in the directions transverse to the wire's length, and not in the longitudinal direction. My question is quite simple. In view of the fact that the derivation of the density of states expression rests upon the assumption that the system is longitudinally confined (correct me if I'm wrong), why is it valid to invoke the result?