Exchange degeneracy

In physical systems consisting of several particles, exchange degeneracy refers to the process in which the system changes the state by exchanging space between two particles , which is degenerate with the original state , i.e. H. has the same energy .

If the number of states at the same energy level increases due to exchange degeneracy, this has measurable consequences. Is it z. B. by a stimulated level , the specific heat increases , because when the temperature increases, not only one state, but also all states that have degenerated with it must be more populated.

Exchange degeneracy for indistinguishable particles

If the exchanged particles are identical , experiments give no indication of the existence of an exchange degeneracy.

The lack of degenerate states for exchanging the same molecules was discovered in the kinetic gas theory at the end of the 19th century and referred to as Gibbs' paradox .

For the electrons in the atomic shell , it was discovered in 1926 in quantum mechanics that their (imaginary) exchange cannot produce a new state, but apparently leaves the initial state unchanged. The fundamental principle in elementary particle physics of the indistinguishability of identical particles is based on this. B. for electrons the well-known Pauli principle follows. Atoms , molecular bonds, semiconductors , black body radiation , white dwarfs and neutron stars cannot be explained otherwise. In the everyday world of experience, however, this complete indistinguishability has no equivalent.

A simple example of such a system is the helium atom, whose atomic shell consists of two electrons. A stationary state should be able to be converted into another two-particle state by permutation of the particles, which should completely agree with the first in terms of energy and all other measurable properties. Because in the case of objects that do not differ physically in any way, the interchange would be an operation that cannot be physically verified. For two electrons this means that their position and spin coordinates have to be exchanged. The exact analysis of the states of the He atom confirms that the exchange of the electrons does not produce a further state.

The mathematical formalism of quantum mechanics takes this into account by the fact that a state vector describes the same state after the interchanging of two indistinguishable particles, i.e. changes at most by one phase factor . The spin statistics theorem further justifies the observation that this phase factor has the constant value −1 for particles of the fermion type and +1 for bosons .