Pauli Exclusion principle.

P. 129.In summary, the Pauli exclusion principle, formulated by Wolfgang Pauli in 1925, states that no two identical fermions can simultaneously occupy the same quantum state. This principle is based on the idea that the wave function of a particle with half-integer spin must be anti-symmetric, while the wave function of a particle with integer spin must be symmetric. This is illustrated by the topological behavior of the lepton wave function, where a rotation of 360 degrees results in a twist and a rotation of 720 degrees brings the object back to its original state. This principle is essential in understanding the behavior of particles on a quantum level and is a key concept in particle physics.
  • #1
_Mayday_
808
0
Having looked into neutrinos and the process in which they were found I've started looking more in Wolfgang Pauli himself. I've read into this principle but there are a few things I would like to clear up. I have picked out the information I am interested in learning abou.

"The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. It states that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement of this principle is that, for two identical fermions, the total wave function is anti-symmetric. For electrons in a single atom, it states that no two electrons can have the same four quantum numbers"

- http://en.wikipedia.org/wiki/Pauli_exclusion_principle

1) These first few questions I am interested more in what the words in bold actually mean. A fermion is a particle with a half integer spin. I know that, but as a fact and do not have any reason to believe that other than I have found it on the internet. What does it mean by half integer spin?

2) What is a wave function, and what would make it anti-symetric?

3) What are quantum numbers?Thanks, any help would be great. I have looked on the wikipedia page but I sometimes get lost reading, as I am not working at a partciularly high level (AS Level) and this is not in the curriculum, but is just out of interest.
 
Physics news on Phys.org
  • #2
What does it mean by half integer spin?
The electron, for instance, carries quantum angular momentun of 1/2 h. h is Plancks constant which has the dimensions of angular momentum.

What is a wave function, and what would make it anti-symetric?
A wave function describes a given physical setup, and allows us to calculate the probabilities of various events, and to make predictions about how the set-up will evolve.

A mathematical function is anti-symmetric is the sign changes on exchanging labels. For instance

x - y is antisymmetric in x, y because swapping x and y changes the sign. x + y is symmetric.

The wave function of a collection of electrons is anti-symmetric under exchange of electrons ( I'm not 100% sure of this, but it's close).

What are quantum numbers?
They are the numbers that describe states in quantum mechanics. Two electrons can't have the same state, therefore they must have different quantum numbers.
 
  • #3
_Mayday_ said:
1) These first few questions I am interested more in what the words in bold actually mean. A fermion is a particle with a half integer spin. I know that, but as a fact and do not have any reason to believe that other than I have found it on the internet. What does it mean by half integer spin?

2) What is a wave function, and what would make it anti-symetric?

3) What are quantum numbers?


Thanks, any help would be great. I have looked on the wikipedia page but I sometimes get lost reading, as I am not working at a partciularly high level (AS Level) and this is not in the curriculum, but is just out of interest.

Pauli exclusion principle
The Pauli exclusion principle can be written in following form: particles of half-integer spin have antisymmetric wavefunctions, and particles of integer spin have symmetric wavefunctions.
In other words the question arise (see Feynman lectures), why "particles with half-integral spin are Fermi particles whose amplitudes add with the minus sign". In his last lecture R. Feynman (Feynman, 1987) sketched an elementary argument for above question, using the topological behaviour of lepton wave function.
There is (Gottfried and Weisskopf, 1986; Gould, 1995) a remarkable property of lepton in three dimensional space: when a lepton is rotated 360 degrees (what means that the wave function phase shifts on 360 degrees), it returns to a state that looks the same geometrically, but that is topologically distinct with respect to its surroundings: a twist has been introduced. A second full rotation (a total of 720 degrees) brings the object back to its original state.
Feyman considered a belt; and the belt ends A and B in two positions 1 and 2 he used for demonstration of rotations of Dirac wave function.
To see this (see fig from R. Feynman paper), first grasp the two ends of a belt, one end in each hand; then interchange the position of your hands. So we have introduced a "twist", which is topologically equivalent to having rotated one end of the belt by 360 degrees.
Thus, when fermions are interchanged, one must keep track of this "implied rotation" and the phase shift, sign change, and destruction interference to which it gives rise. For example, if A(1)B(2) describes "electron 1 in state A and electron 2 in state B," then the state with electrons interchanged must be -A(2)B(1) and their superposition is A(1)B(2) - A(2)B(1)
It could say that according to R. Feynman, if particle field has the Moebius strip topology, it must obey the Pauli exclusion principle..

Feynman, R.P. (1987). The reason for Antiparticles//Elementary particles and the laws of
physics: the 1986 . Dirac Memorial Lectures/. Cambtidge University Press,
1987. – Pp. 1-59.
Gottfried, K. and Weisskopf, V.F. (1984). Concepts of Particle Physics. Oxford.
Gould, Roy R. (1995). Am. J. Phys., Vol 63, No. 2, February
 

1. What is the Pauli Exclusion Principle?

The Pauli Exclusion Principle is a quantum mechanical principle that states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously.

2. What does the Pauli Exclusion Principle explain?

The Pauli Exclusion Principle explains why atoms are stable and do not collapse, as well as why electrons have unique energy levels and orbitals in an atom.

3. Who discovered the Pauli Exclusion Principle?

The Pauli Exclusion Principle was first proposed by Austrian physicist Wolfgang Pauli in 1925.

4. How does the Pauli Exclusion Principle affect the behavior of electrons?

The Pauli Exclusion Principle dictates that electrons in an atom must have different spin states, leading to the formation of electron shells and subshells.

5. What are some practical applications of the Pauli Exclusion Principle?

The Pauli Exclusion Principle is essential for understanding and predicting the properties of atoms and molecules, as well as the behavior of electrons in materials and chemical reactions. It also plays a crucial role in quantum computing and the development of new technologies in the fields of electronics and nanotechnology.

Similar threads

Replies
17
Views
2K
Replies
15
Views
2K
  • Quantum Physics
Replies
2
Views
714
Replies
6
Views
681
  • Quantum Physics
Replies
12
Views
1K
  • Quantum Physics
Replies
2
Views
956
  • Quantum Physics
Replies
6
Views
1K
Replies
9
Views
716
Replies
9
Views
918
  • Quantum Physics
Replies
2
Views
1K
Back
Top