Fermions vs Bosons

In particle physics, there are many ways to classify fundamental particles. One classification is into fermions and bosons. Electrons are an example of fermions while photons are examples of bosons. The difference between fermions and bosons is that two bosons can be in the same quantum state, but two fermions can never occupy the same state (think about electrons in an atom - all of them have at least one quantum number different).

Imagine that you have two bosons and two fermions, and three energy levels available to them: \(0\), \(E_1\) and \(E_2\) (\(E_2\) is not a multiple of \(E_1\)). How many more possible energies can a system of two bosons have than a system of two fermions?

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