Normalization and reduction of the Stark Hamiltonian

TL;DR

This paper presents a method to normalize and reduce the Stark Hamiltonian using Kustaanheimo-Stiefel mapping, resulting in an integrable system with simplified degrees of freedom.

Contribution

It introduces a novel normalization and reduction process for the Stark Hamiltonian leveraging the Kustaanheimo-Stiefel transformation, leading to an integrable reduced system.

Findings

Achieved a second order normal form of the Stark Hamiltonian.

Reduced the system to an integrable two-degree-of-freedom model on $S^2_h imes S^2_h$.

Further simplified to a one-degree-of-freedom Hamiltonian system.

Abstract

This paper details a calculation of the second order normal form of the Stark effect Hamiltonian after regularization, using the Kustaanheimo- Stiefel mapping. After reduction we obtain an integrable two degree of freedom system on $S^2_h \times S^2_h$ , which we reduce again to obtain a one degree of freedom Hamiltonian system.