Abstract: There is no minimal uncertainty in position measurement in the Heisenberg uncertainty principle is to be considered as the minimum of space resolution, whereas numerous theories of quantum gravity predict the existence of a lower bound to the possible resolution of distances. The minimal length is considered commonly by a modification of the Heisenberg uncertainty principle into the generalized uncertainty principle (GUP). The application of GUP modifies every equation of motion of quantum mechanics and consequently, a new window of research has opened to study quantum mechanical problems under the framework of GUP. In this article, we present an exact solution of the Dirac equation with a combined static electric and magnetic field under the framework of GUP and obtain exact energy spectrums. The spectrums manifest a super-symmetry for the sufficient large magnetic field intensity compared to the electric field intensity. The methodology of the solution is designed for convenient implementation of the key property of the harmonic oscillator, the kinetic and potential energy parts of the Hamiltonian are of equal weight. An obligation for the existence of the solution is found that the magnetic field is stronger than the electric field. Our obtained result is confirmed by rendering energy levels of a relativistic electron in an external normal magnetic field, found in the literature.Abstract: There is no minimal uncertainty in position measurement in the Heisenberg uncertainty principle is to be considered as the minimum of space resolution, whereas numerous theories of quantum gravity predict the existence of a lower bound to the possible resolution of distances. The minimal length is considered commonly by a modification of the Heisen...Show More
