We have studied the one‐dimensional (1D) subband energies in quantum wires fabricated on GaAs‐GaAlAs heterostructures. Magnetoresistance oscillations were used to investigate the influence of an applied gate voltage on the 1D subband energies for various geometrical widths of the fabricated quantum wires. For the first time, we measure directly the 1D subband energies by tunneling spectroscopy. As a result, both the confining potential and the influence of an additional magnetic field are well described by a simple harmonic oscillator model.