Because of the discrete conductance steps in split-gate GaAs/Al_(1-x)As quantum point contacts and wires they are commonly referred to as one-dimensional (ID) systems. We discuss what is meant by this characterization by analysing the local density of states (DOS). For realistic device parameters we find that the local DOS may deviate substantially from the ideal ID case, which indicates that the Lieb-Mattis theorem (Lieb and Mattis 1962 Phys. Rev. 125 164), frequently referred to in the present context, does not apply in an obvious way. Spontaneous magnetization due to interactions is therefore feasible, in particular in the vicinity of sublevel thresholds and the associated low electron sub-band densities.
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