Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics

Randal Hallford (Non-Linear Science Research Group, Department of Chemistry & Physics, Midwestern State University, Texas,)
Preet Sharma (Non-Linear Science Research Group, Department of Chemistry & Physics, Midwestern State University, Texas,)

Emerging Science Journal
Vol 4, No 6 (2020): December

The Non-Hermitian aspect of Quantum Mechanics has been of great interest recently. There have been numerous studies on non-Hermitian Hamiltonians written for natural processes. Some studies have even expressed the hydrogen atom in a non-Hermitian basis. In this paper the principles of non-Hermitian quantum mechanics is applied to both the time independent perturbation theory and to the time dependant theory to calculate the Stark effect. The principles of spherical harmonics has also been used to describe the development in the non-Hermitian case. Finally, the non-Hermitian aspect has been introduced to the well known Stark effect in quantum mechanics to find a condition in which the Stark effect will still be true even if a non-Hermitian Hamiltonian is used. This study completes the understanding at a fundamental level to understand the well known Stark effect. Doi: 10.28991/esj-2020-01242 Full Text: PDF