The Stark effect with minimum length

The Covariant Stark Effect

This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schrödinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the nonrelativistic theory. In analogy to the nonrelativistic case, the ...

Stark Effect

An electric field partly lifts the degeneracies of atomic energy levels. This splitting was observed by Stark [1] and explained by Schrödinger [2]. We compute the Stark effect on atomic hydrogen using perturbation theory by diagonalizing the perturbation term in the N-fold degenerate multiplet of states with principal quantum number N . We exploit the symmetries of this problem to simplify the ...

Pruning with Minimum Description Length

The number of parameters in a model and its ability to generalize on the underlying data-generating machinery are tightly coupled entities. Neural networks consist usually of a large number of parameters, and pruning (the process of setting single parameters to zero) has been used to reduce the nets complexity in order to increase its generalization ability. Another less obvious approach is to ...

The Minimum Description Length

The Stark Effect in Hydrogen

In these notes we consider the Stark effect in hydrogen and alkali atoms as a physically interesting example of bound state perturbation theory. The Stark effect concerns the behavior of atoms in external electric fields. We choose hydrogen and alkali atoms because they are single-electron atoms (in the case of alkalis, this is a model). We particularly emphasize the role that symmetry principl...