Eigenvalue of Total Angular Momentum Probability

In summary, eigenvalues are values that represent characteristic properties of a physical system, such as the rotational state in the context of total angular momentum probability. Total angular momentum probability is a measure of the likelihood of a system having a specific total angular momentum value, calculated by finding the eigenvalues of the total angular momentum operator. Eigenvalues play a significant role in providing information about a system's states and probabilities, as well as in calculating other physical properties like energy levels. They are widely applied in various scientific fields, such as quantum mechanics, quantum chemistry, and spectroscopy, to describe the behavior and properties of physical systems.
  • #1
Sekonda
207
0
Hey,

My question is on the probability of attaining a particular eigenvalue for the total angular momentum operator squared for a particular state ψ, the question is shown in the image below:

j_2.png


I believe the eigenvalue of the total angular momentum operator squared is given by j(j+1), which is only equal to 2 when j=1, does this mean the probability of attaining the eigenvalue 2 for the total angular momentum squared is just 1 (i.e. 100%)?

Cheers,
SK
 
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  • #2
Yes, you got it.
 
  • #3
Marvellous! Easier than I thought then, Cheers vela.
 

FAQ: Eigenvalue of Total Angular Momentum Probability

1. What is an eigenvalue?

An eigenvalue is a value that represents a characteristic property of a physical system. In the context of total angular momentum probability, it is a value that describes the rotational state of a system.

2. What is total angular momentum probability?

Total angular momentum probability is a measure of the likelihood that a physical system will have a certain total angular momentum value. It takes into account both the magnitude and direction of the angular momentum.

3. How is total angular momentum probability calculated?

Total angular momentum probability is calculated by finding the eigenvalues of the total angular momentum operator, which is a mathematical representation of the total angular momentum of a system.

4. What is the significance of eigenvalues in total angular momentum probability?

Eigenvalues in total angular momentum probability are important because they provide information about the possible states of a system and their associated probabilities. They can also be used to calculate other important physical properties, such as energy levels.

5. How is the concept of eigenvalues applied in real-world scenarios?

The concept of eigenvalues is widely used in various fields of science, including quantum mechanics, quantum chemistry, and spectroscopy. In these fields, eigenvalues are used to describe the behavior and properties of physical systems, such as atoms and molecules.

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