Bohr’s Quantum Condition Derived From Classical Mechanics and Its Limits of Application

Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. However, this quantum condition was not a logically derived formula. The support of the de Broglie condition was necessary to give physical meaning to Bohr’s quantum condition. However, this paper shows that Bohr’s quantum condition can also be derived from formulas of classical mechanics. Even if an attempt is made to rewrite Bohr’s quantum condition as a relativistic quantum condition, it is not possible to derive the relativistic energy levels of a hydrogen atom. However, if the true quantum condition built into Bohr’s quantum condition is used, then the relativistic energy levels can also be derived, in addition to the nonrelativistic energy levels of a hydrogen atom. In this way we can conclude that the quantum condition vn/c = a/n advocated by this paper is superior as a quantum condition to that of Bohr.