Quantum Gases - Molecular Modelling - page 187

together a space part and a spin part, and it should be clear that there are two possible
results (Table 12.3) and to decide between them we have to resort to experiment. For
many-electron systems, the only states that are ever observed are those that correspond to
antisymmetric total wavefunctions. Heisenberg (1926) recognized this fact and this led to
a detailed understanding of the electronic spectrum and structure of the helium atom. The
condition of antisymmetry eliminates half of the possible states that would otherwise be
possible.

Table 12.3 Combining space and spin functions

Space part Spin part Overall wavefunction

Symmetric Symmetric Symmetric

Antisymmetric Symmetric Antisymmetric

Symmetric Antisymmetric Antisymmetric

Antisymmetric Antisymmetric Symmetric

(When consideringmore than two particles, we have to consider all possible permutations
amongst the space and spin functions.)

12.8 Fermions and Bosons

Not all wavefunctions for identical particles are antisymmetric, but detailed studies show
that, for a given kind of particle, states of only one overall symmetry exist; the states are
either all symmetric or all antisymmetric with respect to interchange of particle names.
Particles whose overall wavefunction is antisymmetric are called fermions (after E. Fermi),
and particles whose overall wavefunction is symmetric are called bosons (after S.N. Bose).
Typical fermions and bosons are shown in Table 12.4.

Table 12.4 Fermions and bosons

Fermion Boson

Electron Photon

Proton Deuteron

Neutron Alpha particle

3 He atom 4 He atom

12.9 Pauli Exclusion Principle

The famous Pauli exclusion principle is a statement of our discussion above; in its general
form it says that fermion wavefunctions must be antisymmetric to exchange of the names
of two fermions, whilst boson wavefunctions must be symmetric. The principle is stated in
different ways in different topics. For example, the world's most popular physical chemistry