Electron spin and the Pauli Exclusion Principle.

In summary, in an atom, only 1 spin up and 1 spin down electron are allowed because you typically choose a basis in a Hilbert space, such as |+1/2> and |-1/2> with respect to the z-direction. However, all other directions are also allowed to define a basis. In an atom with more than one electron, the electrons are in an entangled state and cannot be distinguished as "first" or "second" electron. The state is independent of the choice of direction. This is demonstrated by the identical states with respect to total spin S despite being defined in different directions.
  • #1
Jimmy Snyder
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How is it that only 1 spin up and 1 spin down electron are allowed in an atom even though there is no measurement to collapse the state function?
 
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  • #2
Jimmy Snyder said:
How is it that only 1 spin up and 1 spin down electron are allowed in an atom even though there is no measurement to collapse the state function?
That is not the case.

You typically chose a basis in a Hilbert space. One possibility is |+1/2> and |-1/2> w.r.t. to the z-direction; but all other directions are allowed as well to define a basis.

In addition in an atom with more than one electron (like He² with total spin S=0) it is not true that the "first electron has spin +1/2" and the "second one has spin -1/2" w.r.t. to z. Instead the two electrons are in an entangled state. An ansatz taking antisymmetrization into account is the Slater determinant.

Of course one may chose the z-direction to define the basis; but the state is independent from this choice.
 
  • #3
tom.stoer said:
it is not true that the "first electron has spin +1/2" and the "second one has spin -1/2" w.r.t. to z.
Then how does the third electron 'know' that it can't have spin n,l,m.s = 1,0,0,+1/2 (s w.r.t z)? As you just said yourself, this state is unoccupied.
 
  • #4
Jimmy Snyder said:
Then how does the third electron 'know' that it can't have spin n,l,m.s = 1,0,0,+1/2 (s w.r.t z)? As you just said yourself, this state is unoccupied.

I am only saying that you cannot distinguish between "the first" and "the second" electron. And you should not say that "one electron has spin +1/2 w.r.t. z" whereas "the other one has spin -1/2 w.r.t. z"; that's not wrong but misleading. Both spins couple to S=0. You don't have to mention the z-axis in order to specify the singulet state S=0.

The two states

[tex]|1s,\uparrow_z\rangle|1s,\downarrow_z\rangle - |1s,\downarrow_z\rangle|1s,\uparrow_z\rangle[/tex]

and

[tex]|1s,\uparrow_x\rangle|1s,\downarrow_x\rangle - |1s,\downarrow_x\rangle|1s,\uparrow_x\rangle[/tex]

are identical w.r.t. to total spin S.
 
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1. What is electron spin?

Electron spin is an intrinsic property of an electron that describes its angular momentum and orientation. It is a quantum mechanical property that can have two possible values: spin up and spin down.

2. How is electron spin related to the Pauli Exclusion Principle?

The Pauli Exclusion Principle states that no two electrons in the same atom can have the same set of quantum numbers. This includes the electron spin, which means that if one electron has a spin up, the other electron in the same atom must have a spin down.

3. What is the significance of electron spin in chemistry?

Electron spin plays a crucial role in determining the electronic structure and chemical properties of atoms and molecules. It helps explain the arrangement of electrons in orbitals and the formation of chemical bonds.

4. Can electron spin be measured?

Yes, electron spin can be measured using a technique called electron spin resonance (ESR) spectroscopy. This method uses a magnetic field to interact with the spin of electrons and produce a measurable signal.

5. What are the practical applications of understanding electron spin and the Pauli Exclusion Principle?

Understanding electron spin and the Pauli Exclusion Principle has led to advancements in fields such as materials science, quantum computing, and molecular biology. It also has practical applications in areas such as magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) spectroscopy.

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