Exchange Forces and Symmetrization of Fermions/Bosons

In summary, Griffiths' book explains that the symmetrization of the states of identical fermions and bosons can account for the covalent bonding between two hydrogen atoms to form an H2 molecule. The book discusses how if electrons were bosons, they would tend to congregate between the two nuclei, but since they are fermions, they would do the opposite. The entire state of the particle, including spin and spatial wave function, needs to be antisymmetrical for fermions. However, for covalent bonding to occur, the spatial wave function must be symmetric while the spin states remain antisymmetric. This means that the total wave function for the two electrons must be antisymmetric, but the spatial part must be symmetric
  • #1
zmitchel
1
0
Im reading through Griffiths' Intro to QM book right now, and I can't quite understand a statement he makes about the symmetrization of the states of identical fermions and bosons explaining the covalent bonding between two hydrogen to make an H2 molecule.

The book says that (based on the spatial wave function alone) if electrons were bosons, they would tend to congregate between the two nuclei, which would account for the covalent bonding. Then he explains that since electrons are fermions they would actually do the opposite (again, disregarding spin). Then he says that the entire state of the particle is what needs to be antisymmetrical (since electrons are fermions), which includes spin and the spatial wave function. He concludes by saying that in order for the two-particle system to be conducive to covalent bonding, the spatial wave function must be symmetric and the spin states must be antisymmetric.

My question is how you make the leap from saying that a state reverses its sign when two identical fermions are exchanged, to saying that two identical fermions with antisymmetric spin, but a symmetric wave function, group together.
 
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  • #2
zmitchel said:
...

My question is how you make the leap from saying that a state reverses its sign when two identical fermions are exchanged, to saying that two identical fermions with antisymmetric spin, but a symmetric wave function, group together.

The total wave function above for the two electrons must be antisymmetric, space x spin, but for the hydrogen atoms to bond the space part of the total wave function must be symmetric? Is that correct?

zmitchel, when you use symmetric above does that refer to the space part of the WF or to the total WF?
 

FAQ: Exchange Forces and Symmetrization of Fermions/Bosons

1. What are exchange forces?

Exchange forces refer to the interactions between subatomic particles, such as electrons, that are mediated by the exchange of other particles, such as photons. These forces are responsible for the stability and behavior of matter at the atomic and subatomic level.

2. How do exchange forces affect the symmetrization of fermions and bosons?

Exchange forces play a crucial role in the symmetrization of fermions and bosons. Fermions, which include particles like electrons, follow the Pauli exclusion principle, meaning that no two fermions can occupy the same quantum state. This is due to the exchange forces between fermions, which repel them from occupying the same space. On the other hand, bosons, such as photons, do not follow this principle and can occupy the same quantum state due to their lack of interaction through exchange forces.

3. What is the difference between fermions and bosons in terms of symmetrization?

Fermions and bosons differ in terms of their symmetrization properties due to the exchange forces between them. Fermions have half-integer spin, which leads to their antisymmetric wavefunction, while bosons have integer spin and a symmetric wavefunction. This difference in symmetrization allows for the existence of the Pauli exclusion principle for fermions and the lack of it for bosons.

4. How does the symmetrization of particles affect their properties?

The symmetrization of particles plays a crucial role in determining their properties. For fermions, their symmetrization leads to the Pauli exclusion principle and their stability in atoms and molecules. For bosons, their symmetrization allows for the formation of coherent states, such as in lasers, and the phenomenon of superfluidity.

5. Can the symmetrization of fermions and bosons be observed in everyday life?

Yes, the symmetrization of fermions and bosons can be observed in everyday life. For example, the symmetrization of electrons in atoms leads to the formation of chemical bonds and the stability of matter. The symmetrization of bosons can also be observed in technologies such as lasers and superconductors, which rely on the coherent behavior of bosons due to their symmetric wavefunction.

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