What's the meaning of "totally antisymmetric" in Pauli's Principle?

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In summary, Pauli's Principle defines "totally antisymmetric" as the property of a wave function that changes sign under the interchange of any two particles in a system of identical particles. This requirement is important for accurately describing the behavior of atoms, molecules, and other systems in quantum mechanics. It implies that identical particles cannot occupy the same quantum state simultaneously and is exemplified by the Slater determinant wave function. This concept also relates to the symmetry of physical systems, as the wave function must accurately reflect the symmetries of the system under particle interchange.
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bznm
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Pauli's Principle says:

"The wavefunction of two identical fermions must be totally antisymmetric".

I know that, for a antisymmetric wavefunction,

[itex](-1)^L*(-1)^{S+1}*(-1)^{I+1}=-1[/itex]

"totally antisymmetric" means this relation or it means that these 3 relations:

[itex](-1)^L=-1[/itex] and

[itex](-1)^{S+1}=-1[/itex] and

[itex](-1)^{I+1}=-1[/itex]

must be verified simultaneously?

Thank you!
 
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A system of particles is antisymmetric if it's wavefunction changes sign under exchange of some two particles, it is totally antisymmetric if it does this under exchange of any two.
You should be able to work out the actual conditions from there.
 

1. What is the definition of "totally antisymmetric" in Pauli's Principle?

In Pauli's Principle, "totally antisymmetric" refers to the property of a wave function that describes the state of a system of identical particles. It means that the wave function must change sign under the interchange of any two particles.

2. Why is it important for wave functions to be totally antisymmetric in Pauli's Principle?

The requirement for wave functions to be totally antisymmetric in Pauli's Principle ensures that the wave function accurately describes the behavior of identical particles, which is crucial in understanding the behavior of atoms, molecules, and other systems in quantum mechanics.

3. What does "totally antisymmetric" imply about the behavior of identical particles?

When a wave function is totally antisymmetric, it means that identical particles cannot occupy the same quantum state simultaneously. This leads to the exclusion principle, which states that no two identical fermions can occupy the same quantum state at the same time.

4. Can you provide an example of a wave function that is totally antisymmetric?

One example of a totally antisymmetric wave function is the Slater determinant, which is commonly used to describe the electronic structure of atoms and molecules in quantum chemistry. It satisfies the requirements of Pauli's Principle by changing sign when any two particles are interchanged.

5. How does the concept of "totally antisymmetric" in Pauli's Principle relate to the symmetry of physical systems?

The concept of "totally antisymmetric" in Pauli's Principle is related to the symmetry of physical systems because it ensures that the wave function accurately reflects the symmetries of the system. For example, in a system of two identical particles, the wave function must be antisymmetric under particle interchange, which reflects the symmetry of the system under exchange of the particles.

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