atomic physics Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...

, the central field approximation for many-electron atoms takes the combined electric fields of the

nucleus Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom * Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA Nucl ...

and all the

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...

s acting on any of the electrons to be

radial Radial is a geometric term of location which may refer to: Mathematics and Direction * Vector (geometric), a line * Radius, adjective form of * Radial distance, a directional coordinate in a polar coordinate system * Radial set * A bearing from ...

and to be the same for all the electrons in the atom. That is, every electron sees an identical

potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...

U(r)

that is only a function of its distance from the nucleus. This facilitates an approximate analytical solution to the

eigenvalue In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denot ...

problem for the

Hamiltonian operator Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonia ...

References

Atomic physics {{quantum-stub