Bose Symmetry Explained: Definition & Meaning

[center o bass]

Ive tried to search around for what Bose-symmetry is, but I can't seem to find any definition. Can someone here provide me with a definition of bose symmetry?

 

[electroweak]

Read this: http://en.wikipedia.org/wiki/Exchange_symmetry

We say a multiparticle system has "Bose symmetry" if its wavefunction is invariant under the exchange of identical particles (that is, if its wavefunction is symmetric).

For example, consider a system of two photons with single-particle wavefunctions psi1 and psi2, respectively. The wavefunction of this multiparticle system has the form Psi(x1,x2)=A[psi1(x1)psi2(x2)+psi2(x1)psi1(x2)] where x1 and x2 are the positions of the two particles and A is some normalization constant. Note that this wavefunction is invariant under the exchange of the photons (literally swap x1 and x2 in the above equation and you will get back the original wavefunction). Hence this system has Bose symmetry.

On the other hand, consider a system of two electrons psi1 and psi2. Now our wavefunction is Psi(x1,x2)=A[psi1(x1)psi2(x2)-psi2(x1)psi1(x2)] (note the minus sign), so exchanging the electrons changes the overall sign of the wavefunction. This system does not have Bose symmetry; it has something called Fermi symmetry (antisymmetric wavefunction).

I recommend Chapter 5.1 of Griffiths "Introduction to Quantum Mechanics" for further reading. Good luck!