For the description of a quantum mechanical system of several particles we need an additional
axiom:
5. Quantum mechanical particles are principally indistinguishable.
This
axiom is necessary, because for the description of the complete system we normally use a representation in which the state
of each electron is determined.
Let \(n_i\) be a set of quantum numbers; the complete
state is then described by
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| \begin{equation*} | \psi \rangle = |n_1, n_2, n_3, ...\rangle \end{equation*} | (3.22) |
As long as the system is not disturbed, e.g. by measuring single electrons, no single
electrons exist. Single electrons which may be detected are generated by the measurement. Before a measurement has been
performed no single ”particles” exist.
To emphasize this fact, a system of non-interacting
electrons in a solid is often called ”Jellium”. This describes the non-local character of the electrons. Another
example is the use of the phrase ”Fermi-sea”.
This has to be considered when calculating
many-particle systems.
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© J. Carstensen (Quantum Mech.)