Hydrogen-like atom

A hydrogen-like atom (or hydrogenic atom) is any atom or ion with a single electron. Examples of hydrogen-like atoms are H, He⁺, Li²⁺, Be³⁺ and so on, as well as any of their isotopes. These ions are isoelectronic with hydrogen and are sometimes called hydrogen-like ions. The non-relativistic Schrödinger equation and relativistic Dirac equation for the hydrogen atom and hydrogen-like atoms can be solved analytically, owing to the simplicity of the two-particle physical system. The one-electron wave function solutions are referred to as hydrogen-like atomic orbitals. Hydrogen-like atoms are of importance because their corresponding orbitals bear similarity to the hydrogen atomic orbitals.

The definition of hydrogen-like atoms can be extended to also include any system with only one valence electron (but more core electrons). Examples such atoms include, but are not limited to, all alkali metals such as Rb and Cs and singly ionized alkaline earth metals such as Ca⁺ and Sr⁺. In such a case, the hydrogen-like atom includes a positively charged core consisting of the atomic nucleus and any core electrons, as well as a single valence electron. Because helium is common in the universe, the spectroscopy of singly ionized helium is important in EUV astronomy, for example, of DO white dwarf stars.

Other systems may also be referred to as "hydrogen-like atoms", such as muonium (an electron orbiting an antimuon), positronium (an electron and a positron), certain exotic atoms (formed with other particles), or Rydberg atoms (in which one electron is in such a high energy state that it sees the rest of the atom effectively as a point charge).