The Relationship between the Momentum of an Electron and the Momentum of a Photon Possessed by the Electron, Derived from an Energy-Momentum Relationship Applicable to an Electron inside a Hydrogen Atom
compton wavelength, einstein's energy-momentum relationship, energy-momentum relationship in a hydrogen atom, fine structure constant, momentum of a electron, momentum of a photon
Abstract
Einstein's energy-momentum relationship, which holds in an isolated system in free space, cannot be applied to an electron in a hydrogen atom, where potential energy exists. Thus, the author has previously derived an energy-momentum relationship applicable to an electron in a hydrogen atom. It is possible, by using this relationship, to derive the relationships between the momentum of an electron, and the momentum of a photon possessed by the electron. There is a close relationship between these two physical quantities and the fine structure constant. Also, if the de Broglie relationship is applied to the energy-momentum relationship derived by the author, it is possible to derive the relationship between the wavelength of a moving electron, the wavelength of a photon possessed by the electron, and the Compton wavelength of the electron.
Downloads
How to Cite
References
Bohr (1913) On the Constitution of Atoms and Molecules. 26(1). https://doi.org/10.1080/14786441308634955
Suto (2009) True nature of potential energy of a hydrogen atom. 22, 135-139. https://koshun129.sakura.ne.jp/physics/4spw_index.html
Suto (2018) Potential Energy of the Electron in a Hydrogen Atom and a Model of a Virtual Particle Pair Constituting the Vacuum. 10(4), 93-101. https://doi.org/10.5539/apr.v10n4p93
Suto (2025) Limits on Application of the Formula for Potential Energy of a Hydrogen Atom and a Previously Unknown Formula. 11(3), 1039-1051. https://doi.org/10.4236/jhepgc.2025.113067
Suto (2011) An Energy-Momentum Relationship for a Bound Electron Inside a Hydrogen Atom. 24, 301-307. https://koshun129.sakura.ne.jp/physics/4spw_index.html
Suto (2018) Derivation of a Relativistic Wave Equation More Profound than Dirac's Relativistic Wave Equation. 10, 102-108. https://doi.org/10.5539/apr.v10n6p102
Suto (2020) Theoretical Prediction of Negative Energy Specific to the Electron. 11, 712-724. https://doi.org/10.4236/jmp.2020.115046
Suto (2023) Previously Unknown Formulas for the Relativistic Kinetic Energy of an Electron in a Hydrogen Atom. 11, 972-987. https://doi.org/10.4236/jamp.2023.114065
Suto (2024) The Strange Relationship Between the Momentum of a Photon Emitted from an Electron and the Momentum Acquired by the Electron. 12, 2652-2664. https://doi.org/10.4236/jamp.2024.127157
Suto (2025) The Photon Energy of an Electron with Rest Mass Energy of $m_0 c^2$ is $m_0 c^2$. 17, 44-56. https://doi.org/10.5539/apr.v17n1p44
Einstein (1961) Relativity. 43.
Sommerfeld (1923) Atomic Structure and Spectral Lines. 528.
Suto (2023) Electron Mass in an Atom Is Less than Rest Mass. 11, 3953-3961. https://doi.org/10.4236/jamp.2023.1112252
Suto (2019) The Relationship Enfolded in Bohr's Quantum Condition and a Previously Unknown Formula for Kinetic Energy. 11, 19-34. https://doi.org/10.5539/apr.v11n1p19
Suto (2021) The Quantum Condition That Should Have Been Assumed by Bohr When Deriving the Energy Levels of a Hydrogen Atom. 9, 1230-1244. https://doi.org/10.4236/jamp.2021.96084
Suto (2023) An Energy Level with Principal Quantum Number $n=0$ Exists in a Hydrogen Atom. 23(2), 65-79. https://journalspress.com/LJRS_Volume23/An-Energy-Level-with-Principal-Quantum-Number-n-0-Exists-in-a-Hydrogen-Atom.pdf
Suto (2026) Bohr's Quantum Condition Derived From Classical Mechanics and Its Limits of Application. 18(1), 294-304. https://doi.org/10.5539/apr.v18n1p294
Suto (2020) The Planck Constant Was Not a Universal Constant. 8, 456-463. https://doi.org/10.4236/jamp.2020.83035
Suto (2022) A Surprising Physical Quantity Involved in the Phase Velocity and Energy Levels of the Electron in a Hydrogen Atom. 14(2), 1-17. https://doi.org/10.5539/apr.v14n2p1
Suto (2014) Previously Unknown Ultra-low Energy Level of the Hydrogen Atom Whose Existence can be Predicted. 6(6), 64-73. https://doi.org/10.5539/apr.v6n6p64
Published
2026-09-23
Issue
Section
License
Copyright (c) 2026 Authors and Global Journals Private Limited
This work is licensed under a Creative Commons Attribution 4.0 International License.