The Noncommutative Quadratic Stark Effect For The H-Atom

TL;DR

This paper calculates the second order noncommutative Stark effect on the hydrogen atom's ground state energy using perturbation theory and exact methods, revealing noncommutative influences on energy shifts and polarizability.

Contribution

It provides the first detailed computation of the noncommutative quadratic Stark effect for hydrogen, including a sum rule for oscillator strength.

Findings

Energy shift is quadratic in electric field and noncommutative parameter.

Noncommutative effects cause the polarizability to become non-diagonal.

Derived a sum rule for mean oscillator strength.

Abstract

Using both the second order correction of perturbation theory and the exact computation due to Dalgarno-Lewis, we compute the second order noncommutative Stark effect,i.e., shifts in the ground state energy of the hydrogen atom in the noncommutative space in an external electric field. As a side result we also obtain a sum rule for the mean oscillator strength. The energy shift at the lowest order is quadratic in both the electric field and the noncommutative parameter $\theta$. As a result of noncommutative effects the total polarizability of the ground state is no longer diagonal.