Ground state of the hydrogen atom via Dirac equation in a minimal-length scenario

Abstract

In this work we calculate the correction to the ground state energy of the hydrogen atom due to contributions arising from the presence of a minimal length. The minimal length scenario is introduced by means of modifying the Dirac equation through a deformed Heisenberg algebra (kempf algebra). With the introduction of the Coulomb potential in the new Dirac energy operator, we calculate the energy shift of the ground state of the hydrogen atom in first order of the parameter related to the minimal length via perturbation theory.

Towards quantum mechanics on the curved cotangent bundle

“…For the hydrogen atom, where M denotes the mass of the electron, this corresponds to a value δE nlm ∼ 10 −44 as had been reported before in the context of the GUP [130][131][132]. This result can be improved upon by applying it to more massive charged particles such as the W ± , yielding δE nlm ∼ 10 −35 .…”

“…Gravitational corrections, both quantum and classical, to quantum mechanical experiments are usually negligibly small. For instance, the relative correction of the earth's gravitational field to the energy spectrum of the hydrogen atom is of the order 10 −38 [129], while the corresponding magnitude stemming from a Planckian GUP is expected to lie around 10 −44 [130][131][132]. Thus, it suffices to treat the corresponding effects perturbatively, i.e.…”