Idential particles, postion wavefunction for fermions.

In summary, the chapter on identical particles in Griffiths' book states that the wavefunction for two particles can either be + or - depending on whether they are bosons or fermions. However, in class it was observed that for two electrons in a spin singlet state, the position part of the wavefunction does not change sign when the particles are swapped, only the spin part does. This raises the question of whether Griffiths is ignoring spin in the mentioned identity. Upon further investigation, it is found that in the first edition of the book, Griffiths does state that he will ignore spin at this point, but later brings it in.
  • #1
Coffee_
259
2
1. In griffiths the following is written down in the chapter of identical particles:

##\Psi(\vec{r_{1}},\vec{r_{2}})=\pm \Psi(\vec{r_{2}},\vec{r_{2}})##

Where it's + for bosons and - for fermions.

However in class we have seen that for two electrons in the spin singlet situation the POSITION part of their wavefunction doesn't change signs upon swapping the particles. It's the spin part that changes sign in that case.

How to concile these two results? Does Griffiths take spin into account when writing the mentioned identity above? Because at least it looks like he means the position parts of the wavefunctions at first glance.
 
Physics news on Phys.org
  • #2
Check to see if Griffiths is ignoring spin at this point of the text. In the first edition, he says at the beginning of the chapter, "we'll ignore spin for the moment". Quite a bit later in the chapter, he brings in spin.
 
  • #3
TSny said:
Check to see if Griffiths is ignoring spin at this point of the text. In the first edition, he says at the beginning of the chapter, "we'll ignore spin for the moment". Quite a bit later in the chapter, he brings in spin.

Oh yes, you are entirely correct. I should have searched a bit longer in the book before posting. Thanks.
 

1. What are identical particles?

Identical particles are particles that cannot be distinguished from one another based on their physical properties, such as mass, charge, and spin. Examples of identical particles include electrons, protons, and neutrons.

2. What is the position wavefunction for fermions?

The position wavefunction for fermions is a mathematical function that describes the probability of finding a fermion at a particular position in space. It is often denoted by the symbol Ψ and is used to calculate the probability of finding a fermion within a certain volume or at a specific location.

3. How does the position wavefunction differ for fermions compared to bosons?

The position wavefunction for fermions differs from that of bosons due to the Pauli exclusion principle, which states that no two fermions can occupy the same quantum state at the same time. This results in the position wavefunction for fermions being antisymmetric, while the position wavefunction for bosons is symmetric.

4. What is the significance of the position wavefunction for fermions?

The position wavefunction for fermions is significant because it allows us to understand and predict the behavior of identical particles. It also plays a crucial role in quantum mechanics and is used in many calculations, such as determining the energy levels of atoms and molecules.

5. How is the position wavefunction for fermions experimentally determined?

The position wavefunction for fermions can be experimentally determined through techniques such as electron diffraction or scanning tunneling microscopy. These methods involve sending a beam of particles towards a sample and measuring the resulting diffraction pattern or tunneling current, which can then be used to calculate the position wavefunction of the fermions in the sample.

Similar threads

Replies
16
Views
1K
  • Advanced Physics Homework Help
Replies
9
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
778
  • Advanced Physics Homework Help
Replies
26
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
927
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Quantum Physics
Replies
2
Views
767
  • Quantum Physics
Replies
11
Views
2K
Back
Top