High Quality Content by WIKIPEDIA articles! A quantum state is a set of mathematical variables that fully describes a quantum system. For example, the set of 4 numbers {, , , } defines the state of an electron within a hydrogen atom and are known as the electron`s quantum numbers. Other examples could be "given direction and energy, or some other given condition", when we are talking about scattering. More generally, the state of the system is represented by a single vector known as a ket.