Suppose we have particles of kind B, that consist of two fermions of kind F. Now the particles B satisfy the Bose statistics. But what precisely does this mean? If we have four F particles, the system is described by a wave function(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\psi(x_1,x_2,x_3,x_4)

[/tex]

Suppose the particles 1 and 2 are bounded and form one particle B, and 3 and 4 are bounded too. Then it should be possible to approximate this system as a two particle system

[tex]

\approx \psi'(x_{12}, x_{34})

[/tex]

where [itex]x_{12}[/itex] and [itex]x_{34}[/itex] are some kind of approximate coordinates for the particles B.

How can these ideas made more rigor? We have

[tex]

\psi(x_{\sigma(1)}, x_{\sigma(2)}, x_{\sigma(3)}, x_{\sigma(4)}) = \varepsilon(\sigma) \psi(x_1,x_2,x_3,x_4),

[/tex]

and we want to prove

[tex]

\psi'(x_{12}, x_{34}) = \psi'(x_{34}, x_{12}).

[/tex]

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# Fermi and Bose statistics

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