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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Format: | Article |
Language: | English |
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Ital Publication
2020-12-01
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Series: | Emerging Science Journal |
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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 |
first_indexed | 2024-12-21T11:20:08Z |
format | Article |
id | doaj.art-c73a28ef1d5f4c01a98a544308ce102c |
institution | Directory Open Access Journal |
issn | 2610-9182 |
language | English |
last_indexed | 2024-12-21T11:20:08Z |
publishDate | 2020-12-01 |
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series | Emerging Science Journal |
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 |
work_keys_str_mv | AT randalhallford nonhermitianhamiltoniantreatmentofstarkeffectinquantummechanics AT preetsharma nonhermitianhamiltoniantreatmentofstarkeffectinquantummechanics |