Question about the Pauli exclusion principle.

In summary, the conversation discusses the generation of an infinite number of states from only two states through linear combinations. However, for a two particle state, there can only be one allowed state due to the Pauli exclusion principle, which requires the wavefunction to be antisymmetric. This means that while there are only two possible basis states for an electron's spin, there can be an infinite number of spin states through linear combinations.
  • #1
alemsalem
175
5
Suppose there are only two states, and that only two electrons could fit in them (spin states for example), but wouldn't these two states form a basis and so generate an infinite number of states that are linear combinations of these two, so three electrons could be in three different states.

Obviously that's wrong, but why? do they have to be in orthogonal states?
 
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  • #2
The Pauli exclusion principle arises from the requirement that the wavefunction of the system be antisymmetric under the exchange of fermionic degrees of freedom. Now you may try to write down the wavefunction with three particles, but you'll find that the antisymmetry property causes such a wavefunction to vanish.
 
  • #3
alemsalem said:
Suppose there are only two states, and that only two electrons could fit in them (spin states for example), but wouldn't these two states form a basis and so generate an infinite number of states that are linear combinations of these two, so three electrons could be in three different states.

Obviously that's wrong, but why? do they have to be in orthogonal states?


I think there is some confusion here. There are two states, yes, so in principle, you can form an infinite number of states through linear combinations, but those are one particle states.

For a two particle state, the only one allowed is the state where one particle is spin up and the other is spin down. There is only one state for for the combined system.

I hope that helps.
 
  • #4
Should i forward a conclusion that linear combination of the spin functions of the electron cannot be done: that means ultimately there are only 2 possible spin states for an electron ! Anyone can further comment this ?
 
  • #5
gerrardz said:
Should i forward a conclusion that linear combination of the spin functions of the electron cannot be done: that means ultimately there are only 2 possible spin states for an electron ! Anyone can further comment this ?

There are only two possible BASIS states for the spin states for an electron since they are spin 1/2. However, there an infinite number of spin states for an electron because you can make any number of other states by performing a linear combination of these 2 states.

I hope I got your question correct.
 

What is the Pauli exclusion principle?

The Pauli exclusion principle is a fundamental principle in quantum mechanics that states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. This means that two electrons, for example, cannot have the same set of quantum numbers (such as energy level, orbital shape, and spin) in an atom.

Why is the Pauli exclusion principle important?

The Pauli exclusion principle is important because it explains many properties of matter, such as the stability of atoms and the periodic table of elements. It also plays a crucial role in understanding the behavior of electrons in materials, which is important in fields such as chemistry and electronics.

What evidence supports the Pauli exclusion principle?

The Pauli exclusion principle has been tested and confirmed through various experiments, such as the Stern-Gerlach experiment, which showed that electrons have two possible spin states. Additionally, the principle is also supported by the successful predictions and explanations it provides for various phenomena in quantum mechanics.

Are there any exceptions to the Pauli exclusion principle?

While the Pauli exclusion principle holds true for most cases, there are a few exceptions. For example, in certain extreme conditions, such as in neutron stars, the high pressure can cause electrons to merge into a single quantum state, violating the principle.

How does the Pauli exclusion principle relate to the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle states that it is impossible to know the exact position and momentum of a particle simultaneously. This uncertainty is due to the wave-like nature of particles. The Pauli exclusion principle adds to this uncertainty by limiting the number of possible states a particle can occupy, thus adding to the uncertainty of its position and momentum.

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