Helium atom  A helium atom is an atom of the chemical element helium. Helium is composed of two electrons bound by the electromagnetic force to a nucleus containing two protons along with either one or two neutrons, depending on the isotope, held together by the strong force. Unlike for hydrogen, a closed-form solution to the Schrödinger equation for the helium atom has not been found. However, various approximations, such as the Hartree–Fock method, can be used to estimate the ground state energy and wavefunction of the atom. The quantum mechanical description of the helium atom is of special interest, because it is the simplest multi-electron system and can be used to understand the concept of quantum entanglement. The Hamiltonian of helium, considered as a three-body system of two electrons and a nucleus and after separating out the centre-of-mass motion, can be written as  where formula_2 is the reduced mass of an electron with respect to the nucleus, formula_3 and formula_4 are the electron-nucleus distance vectors and formula_5. The nuclear charge, formula_6 is 2 for helium. In the approximation of an infinitely heavy nucleus, formula_7 we have formula_8 and the mass polarization term formula_9 disappears. In atomic units the Hamiltonian simplifies to  It is important to note, that it operates not in normal space, but in a 6-dimensional "configuration space formula_11". In this approximation (Pauli approximation) the wave function is a second order spinor with 4 components formula_12, where the indices formula_13 describe the spin projection of both electrons ("z"-direction up or down) in some coordinate system. It has to obey the usual normalization condition formula_14. This general spinor can be written as 2x2 matrix formula_15 and consequently also as linear combination of any given basis of four orthogonal (in the vector-space of 2x2 matrices) constant matrices formula_16 with scalar function coefficients formula_17 as formula_18. A convenient basis consists of one anti-symmetric matrix (with total spin formula_19, corresponding to a singlet state)formula_20 and three symmetric matrices (with total spin formula_21, corresponding to a triplet state) formula_22 formula_23 formula_24It is easy to show, that the singlet state is invariant under all rotations (a scalar entity), while the triplet can be mapped to an ordinary space vector formula_25, with the three componentsformula_26, formula_27 and formula_28.Since all spin interaction terms between the four components of formula_29 in the above (scalar) Hamiltonian are neglected (e.g. an external magnetic field, or relativistic effects, like angular momentum coupling), the four Schrödinger equations can be solved independently.