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 coupling of an electromagnetic field the connections to the energy levels of the electron in a Pening trap caused by the gravitational field of the Earth are computed. Our discussion shows that the resulting effect is detectable only at the specific eigenfrequencies of the electron. The relative shift of these frequencies due to the gravitational field is found to be 2.1 x 10(-9). It is briefly indicated how this effect in principle could be observed in suitable experiments performed with higher precision. These results have been published in [1].