The two-terminal conductance of ballistic point contacts in the two-dimensional electron gas of a high-mobility GaAs/Al x Gai_^As heterostructure has been studied in quantizing electric and magnetic fields. The conductance is found to be quantized at multiples of e 2 /h, exclusively determined by the number of occupied magnetoelectric subbands in the constriction. The experiment provides the first direct demonstration of magnetic and electric depopulation of one-dimensional subbands in a single wire.The study of ballistic electron transport in small semiconductor devices is a rapidly developing field of research.'~5 Combining present-day microfabrication technology and advanced material growth techniques, such äs molecular-beam epitaxy, devices can be made through which electrons can travel with a minimal amount of impurity scattering. These Systems are ideal for the study of quantum transport, which occurs in devices with dimensions comparable to the wavelength of the carriers. A clear manifestation of quantum transport has been reported in Ref. 6. The two-terminal conductance of narrow and short ballistic constrictions (point contacts) in a two-dimensional electron gas (2D EG) changes in steps of 2e 2 /h, when the width is varied by means of a gate.Because of the ballistic transport in the constriction, a direct correspondence between the conductance and the number of occupied subbands in the constriction is observed, each subband contributing an amount 2e 2 /h to the conductance. This makes these devices very suitable for the study of the (quasi-)one-dimensional subband structure in narrow wires. This can be done either by electric depopulation, reducing the number of occupied subbands by decreasing the width (or the electron density) of the wire, or by magnetic depopulation. A perpendicular magnetic field forms hybrid magnetoelectric subbands, which can be depopulated by increasing the field.Electric depopulation in devices containing many identical parallel wires has been reported by Warren, Antoniadis, and Smith. 7 Many parallel wires were required to average out the irregulär resistance fluctuations that mask the structure due to the subband depopulation in a single wire. These fluctuations are a result of random quantum interference, which is inevitably present in Systems containing randomly distributed impurities. Alternatively, the quasi-1D subband structure has been studied by infrared spectroscopy 8 and by capacitive techniques. 9 Both also require a multiwire System to resolve the signal originating from the depopulation of subbands.Magnetic depopulation has been studied in single wires 10 '" by measuring the deviations from the \/B periodicity of the Shubnikov-de Haas resistance oscillations at low fields, the observation of which is also made difficult by the irregulär structure in the magnetoresistance. Moreover, it is not possible to determine the number of occupied subbands at zero field from the measurements.In the point contacts we study in this paper, the number of occupied subbands can be d...