For a multielectron atom such as He, Li, etc. the Schrödinger equation may be written as H
= E where H is the operator representing the kinetic and potential energies of
all the particles and and E are the wavefunction and energy respectively. For a helium atom, keeping the nucleus fixed (this is not a bad approximation since the nuclei are much heavier than the electrons) H can be written as
(6.1)
The first two terms correspond to the kinetic energy of electrons 1 and 2, the third and fourth are the interaction energies of the two electrons with the He nucleus and the last term is the electron - electron repulsion. Here
Figure 6.3 The coordinates of the two electrons in He atom
The solution of equation (6.1) is the wavefunction
= (1,2) or (r1, r2 ) = (x1, y1, z1, x2, y2, z2 ). This is a function of six variables and is difficult to handle. A good way to approximate this is to write it as
(r1 ,r2 ) = 1 (r1 ). 2 (r 2 ),
(6.2)
which is a product of orbitals 1 (r1) depending on the coordinate of the first electron and 2 (r2), which depends on the coordinates of the second electron. Wavefunctions refer to the solutions of the Schrödinger equation while orbitals refer to the function of the coordinates of a single electron and are the solutions to an approximate or an effective equation which is described below.
= E
1 (r
2 (r 2 ),
2 (r2), which depends on the coordinates of the second electron. Wavefunctions refer to the solutions of the Schrödinger equation while orbitals refer to the function of the coordinates of a single electron and are the solutions to an approximate or an effective equation which is described below. 
