Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics

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...

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Main Authors: Randal Hallford, Preet Sharma
Format: Article
Language:English
Published: Ital Publication 2020-12-01
Series:Emerging Science Journal
Subjects:
Online Access:https://ijournalse.org/index.php/ESJ/article/view/394
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author Randal Hallford
Preet Sharma
author_facet Randal Hallford
Preet Sharma
author_sort Randal Hallford
collection DOAJ
description 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
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spelling doaj.art-c73a28ef1d5f4c01a98a544308ce102c2022-12-21T19:05:48ZengItal PublicationEmerging Science Journal2610-91822020-12-014642743510.28991/esj-2020-01242151Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum MechanicsRandal Hallford0Preet Sharma1Non-Linear Science Research Group, Department of Chemistry & Physics, Midwestern State University, Texas,Non-Linear Science Research Group, Department of Chemistry & Physics, Midwestern State University, Texas,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: PDFhttps://ijournalse.org/index.php/ESJ/article/view/394quantum mechanicsnon-hermitian hamiltonianshydrogen atomstark effectspherical harmonics.
spellingShingle Randal Hallford
Preet Sharma
Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics
Emerging Science Journal
quantum mechanics
non-hermitian hamiltonians
hydrogen atom
stark effect
spherical harmonics.
title Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics
title_full Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics
title_fullStr Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics
title_full_unstemmed Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics
title_short Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics
title_sort non hermitian hamiltonian treatment of stark effect in quantum mechanics
topic quantum mechanics
non-hermitian hamiltonians
hydrogen atom
stark effect
spherical harmonics.
url https://ijournalse.org/index.php/ESJ/article/view/394
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