Why do we use the hydrogen system approximation in quantum mechanics?

The hydrogen system approximation is particularly useful in quantum mechanics because it simplifies the calculations for complex systems. The hydrogen atom, being the simplest atom with only one electron, allows for an exact solution to the Schrödinger equation, which in turn facilitates a clearer understanding of quantum mechanics and atomic structure.

In more complex atoms, the presence of multiple electrons introduces electron-electron interactions that complicate the mathematical treatment significantly. By studying the hydrogen atom, researchers can gain valuable insights and develop foundational principles that can be later applied to more complicated systems. These principles help physicists and chemists make approximations or use perturbation theory when addressing larger systems, effectively building on the simplicity afforded by the hydrogen model.

While the hydrogen atom serves as a fundamental reference, it is not accurate to say that all atoms behave exactly like hydrogen, nor does this approximation necessarily enhance the accuracy of energy levels for more complex atoms. Additionally, the approximation is not limited solely to one-electron atoms; it establishes a basis from which further, more complex theories can be developed.