bigubau said:It was actually solved algebraically in 1925 by Wolfgang Pauli. See the pages 235 up to 244 of Kurt Gottfried's book on QM (2nd edition, 2003).
alxm said:There was the Bohr and Bohr-Sommerfeld models. But there was no model that got the QM result prior to Schrödinger, I'm almost certain.
bigubau said:A better account on the algebraic solution for the H-atom can be found in Biedenharn's "Theory of angular momentum", Vol 1, Chapter 7, dection 4. A detailed bibliography can be found at the end of the section.
Avodyne said:
The hydrogenic atom is a type of atom that has only one electron and is similar to the hydrogen atom. It is considered a simplified model for other atoms, as it only contains a nucleus (with a single proton) and an electron.
The hydrogenic atom can be solved algebraically by using the Schrodinger equation, which is a mathematical equation that describes the behavior of quantum particles, such as electrons. By solving this equation for the hydrogenic atom, we can determine the energy levels and wavefunctions of the electron.
The algebraic solution of the hydrogenic atom allows us to understand and predict the behavior of electrons in other atoms and molecules. It also provides a foundation for the study of quantum mechanics and helps us understand the properties of matter at a microscopic level.
The algebraic solution of the hydrogenic atom only applies to atoms with one electron, so it cannot be used to solve more complex systems. It also does not take into account the effects of relativity, which become significant for heavier elements.
The algebraic solution of the hydrogenic atom provides the basis for understanding the organization of the periodic table. The energy levels and wavefunctions of electrons in different atoms can be mapped onto the periodic table, allowing us to predict the properties of elements based on their position in the table.