Possible values of total angular momentum of a 2 electron system

In summary, the possible total spin values are 1 and 0, and the total angular momentum in the z-direction can be 1, 0, or -1. The inequality \mid l-s\mid\leq j\leq l+s\: ,\: -j\leq m_{z}\leq j is used to determine the maximum value of 'j' and the possible values of 'm' in integer steps. It is also noted that S=1 corresponds to m=1, 0, or -1 and S=0 corresponds to m=0.
  • #1
Sekonda
207
0
Hey,

Also a bit confused on this one, the question is displayed below

2elec.png


The possible total spin values are 1,0,-1 and I know that

[tex]\mid l-s\mid\leq j\leq l+s\: ,\: -j\leq m_{z}\leq j[/tex]

Where the latter inequality is in integer steps, so I'm not really sure if it is as simple as substituting in the 's' values into the first inequality and then using the maximum 'j' value in the second inequality.

Probably didn't make any sense.

Any help is appreciated!
SK
 
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  • #2
Hmm actually is it that the total spin can be either 1 or 0, and the total angular momentum in the z-direction can be 1,0,-1.

So S=1 goes to m=1,0,-1 and S=0 goes to m=0?

Or is that wrong...

Cheers,
SK
 
  • #3
Sekonda said:
Hmm actually is it that the total spin can be either 1 or 0, and the total angular momentum in the z-direction can be 1,0,-1.

So S=1 goes to m=1,0,-1 and S=0 goes to m=0?

Or is that wrong...

Cheers,
SK

This is the correct answer. Very good!
 

Related to Possible values of total angular momentum of a 2 electron system

1. What is total angular momentum in a 2 electron system?

Total angular momentum is a measure of the overall rotational motion of a system. In a 2 electron system, it takes into account the individual angular momenta of each electron as well as their combined motion.

2. What are the possible values of total angular momentum in a 2 electron system?

The possible values of total angular momentum in a 2 electron system depend on the quantum numbers of the electrons. The maximum value is given by the sum of the maximum individual angular momenta, while the minimum value is given by the difference between the maximum and minimum individual angular momenta.

3. How do the individual angular momenta of the electrons affect the total angular momentum in a 2 electron system?

The individual angular momenta of the electrons can combine in different ways to give different values of total angular momentum. For example, if both electrons have the same angular momentum, the total angular momentum will be twice that value. If one electron has an angular momentum of 0, the total angular momentum will be equal to the other electron's angular momentum.

4. Can the total angular momentum of a 2 electron system be greater than the sum of the individual angular momenta?

Yes, the total angular momentum of a 2 electron system can be greater than the sum of the individual angular momenta. This is because the electrons can have different orientations and their angular momenta can add or subtract from each other to give a larger total value.

5. How does the total angular momentum of a 2 electron system affect its properties?

The total angular momentum of a 2 electron system can affect its properties in many ways. It can determine the energy levels of the system, the direction of the system's rotation, and the shape of its orbit. It can also affect the system's magnetic properties and how it interacts with other particles and fields.

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