We present results of a detailed study of equilibrium magnetotunneling
between an array of independent identical one-dimensional wires and a
two-dimensional electron gas. From the tunneling differential conduct
ance, measured as a function of the in-plane magnetic field, we find d
irectly the number of occupied one-dimensional subbands, the subband e
nergies, and the wave functions as a function of the strength of confi
nement in these wires. As many as 14 one-dimensional subbands were pro
bed. We show that an analysis of our results based on the Bardeen tunn
eling Hamiltonian formalism allows the determination of the functional
form of one-dimensional confining potentials. We give two examples, o
ne for a narrow wire and one for a wide wire.