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Suto, K. (2021) The Quantum Condition That Should Have Been Assumed by Bohr When Deriving the Energy Levels of a Hydrogen Atom. Journal of Applied Mathematics and Physics, 9, 1230-1244.
https://doi.org/10.4236/jamp.2021.96084

has been cited by the following article:

• TITLE: Previously Unknown Formulas for the Relativistic Kinetic Energy of an Electron in a Hydrogen Atom

  AUTHORS: Koshun Suto

  KEYWORDS: Einstein’s Energy-Momentum Relationship, Relativistic Kinetic Energy, Bohr’s Quantum Condition, Potential Energy, Phase Velocity, Group Velocity

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.4, April 26, 2023

  ABSTRACT: Einstein’s energy-momentum relationship, which holds in an isolated system in free space, contains two formulas for relativistic kinetic energy. Einstein’s relationship is not applicable in a hydrogen atom, where potential energy is present. However, a relationship similar to that can be derived. That derived relationship also contains two formulas, for the relativistic kinetic energy of an electron in a hydrogen atom. Furthermore, it is possible to derive a third formula for the relativistic kinetic energy of an electron from that relationship. Next, the paper looks at the fact that the electron has a wave nature. Five more formulas can be derived based on considerations relating to the phase velocity and group velocity of the electron. This paper presents eight formulas for the relativistic kinetic energy of an electron in a hydrogen atom.