INFLUENCE OF THE GRAVITATIONAL-FIELD ON THE QUANTUM STATES OF THE ELECTRON IN A PENNING TRAP

Starting from the general covariant Dirac equation with minimal coupli ng of an electromagnetic field the corrections to the energy levels of the electron in a Penning trap caused by the gravitational field of t he Earth are computed. Our discussion shows that the resulting effect is detectable only at the specific eigenfrequencies of the electron. T he relative shift of these frequencies due to the gravitational field is found to be 2.1x10(-9). It is briefly indicated how this effect in principle could be observed in suitable experiments performed with hig her precision.