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.