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In summary: The half-integer spin particles are fermions because their wavefunction is antisymmetric, while the integer spin particles are bosons because their wavefunction is symmetric.

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So what fundamentally makes fermions and bosons different?

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Thanks man. I'll check it out.

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Young physicist said:

I think your question here exhibits a deeper issue than simply the Fermi-Dirac statistics.

The world that you see around you arises out of the collective behavior of a gazillion particles. You never deal with just one, or a few particles or interactions. Now, it is impossible to know the dynamics of every single one of these particles. So instead, we find a description of their

You also do not need to delve into quantum physics to talk about statistics of particles. The basic thermodynamics laws are based on the classical description of particles via the Maxwell-Boltzmann statistics. So even before QM, we are already well-aware of statistical mechanics.

Zz.

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https://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem said:Bosons are particles whose wavefunction is symmetric under such an exchange or permutation, so if we swap the particles the wavefunction does not change. Fermions are particles whose wavefunction is antisymmetric, so under such a swap the wavefunction gets a minus sign, meaning that the amplitude for two identical fermions to occupy the same state must be zero. This is the Pauli exclusion principle: two identical fermions cannot occupy the same state. This rule does not hold for bosons.

From that "simple" difference, the statistics arise.

Fermi-Dirac statistics, also known as Fermi statistics, is a branch of quantum statistics that describes the behavior of a large number of identical particles with half-integer spin, such as electrons, protons, and neutrons.

Fermi-Dirac statistics differ from other statistical models, such as Bose-Einstein statistics, in that they take into account the exclusion principle, which states that two identical fermions cannot occupy the same quantum state simultaneously. This leads to a unique distribution of particles and their energies.

While the mathematics behind Fermi-Dirac statistics can be complex, the concept itself is fairly straightforward. It is based on the idea that particles with half-integer spin follow different rules than particles with integer spin, and their behavior is influenced by the exclusion principle.

Fermi-Dirac statistics are used to understand and predict the behavior of fermionic systems, such as electrons in a solid material. This has important applications in fields such as condensed matter physics, materials science, and electronics.

While Fermi-Dirac statistics accurately describe the behavior of fermionic systems in most cases, they do have some limitations. For example, they do not take into account the effects of interactions between particles, which can become significant at high densities or temperatures.

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