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

作　　者：Koshun Suto Koshun Suto(Chudai-Ji Temple, Isesaki, Japan)

机构地区：[1]Chudai-Ji Temple, Isesaki, Japan

出　　处：《Journal of Applied Mathematics and Physics》2023年第4期972-987,共16页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Einstein’s Energy-Momentum Relationship Relativistic Kinetic Energy Bohr’s Quantum Condition Potential Energy Phase Velocity Group Velocity 

分 类 号：O57[理学—粒子物理与原子核物理]