Uncertainty relation of the momentum components of a two-dimensional electron system under a tilted magnetic field


A two-dimensional electron gas along the xy-plane is considered. When an applied perpendicular magnetic field, directed along the z-axis, is turned on, the electrons move in cyclotron orbits and the components of the momentum along the x- and y-axes do not commute. This work shows that if the applied magnetic field is tilted at an angle θ with respect to the z-axis, the uncertainty in simultaneous measurements of the momentum components becomes dependent on θ.