In 1926, Erwin Schrödinger proposed an equation that describing the wave function for the electron orbits of the Hydrogen atom. The Schrödinger equation is accepted as a postulate because of unclear and possible erroneous steps in his methods. Addressing the erroneous steps, we show that the Schrödinger equation extracts only the stable trajectories from all possible trajectories that are solutions of the Hamilton-Jacobi equation. This approach applied to a Hydrogen atom leads to the following results: (1) Bohr orbits are stable, (2) the electron’s spin in an atom is precessing; (3) the energy of the precessional motion on Bohr orbits satisfies the Rydberg’s formula.
[See the full post at: The Schrödinger equation from the point of view of the theory of stability]