The energy spectra of isolated one-dimensional (ID) electron channels have been studied by photoluminescence in zero and finite magnetic fields B. Arrays of periodic quantum wires (period =290-400 nm, width = 150-170 nm) were etched from modulation-doped AlvGai-vAs/GaAs heterojunctions, with special low-concentration Be 5 doping in the buffer layer to increase the photoluminescence intensity. We were able to attain the ID quantum limit, i.e., occupation of only the lowest ID subband at 5=0, and to measure, at small B, a characteristic quadratic B dispersion of the 1D subband edge.