The Relationship Between Angular Momentum and Quantum Numbers

In summary, the conversation discusses the possible values of total angular momentum for two particles with orbital angular momentum quantum numbers, as well as the probability of finding these values. Additionally, it mentions the total spin and angular momentum of a system with two spin 1/2 fermions.
  • #1
Chinnu
24
0
Heres the problem:

Part I) Two particles, each with orbital angular momentum quantum numbers l=1,
m sub l = 0. What are the possible values of the total angular momentum? What is the probability that a measurement will find each of these values?

Part II) Consider the case where the two particles are spin 1/2 fermions. Neglect their interaction and assume that they both have the same radial wave function. What are the total spin and the total angular momentum of the system?


For part I, I think the possible values for the total orbital angular momentum are |l1+l2| down to 0. Meaning, 2, 1, and 0.
Im not sure how to get the probabilities though. I think I have to use Clebsch-Gordon coefficients, but I am not entirely sure how to do that I guess.
 
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  • #2
For part II, the total spin of the system is 1, since the particles are both spin 1/2 fermions. The total angular momentum of the system is also 1, since the two particles have the same radial wave function and their orbital angular momenta cancel out.
 

FAQ: The Relationship Between Angular Momentum and Quantum Numbers

What is angular momentum?

Angular momentum is a property of a rotating object that measures the amount of rotational motion it possesses. It is a vector quantity that depends on an object's mass, velocity, and distance from the axis of rotation.

What is the angular momentum problem?

The angular momentum problem is a fundamental issue in physics that arises when trying to explain the stability of rotating systems, such as planetary orbits and spinning objects. It is the discrepancy between classical mechanics, which predicts that these systems should become unstable and collapse, and observed reality.

How is the angular momentum problem solved?

The angular momentum problem is solved by incorporating the principles of quantum mechanics and relativity into the classical theory of mechanics. This leads to the development of new theories, such as quantum mechanics and general relativity, which can explain the stability of rotating systems.

What is the importance of the angular momentum problem?

The angular momentum problem is important because it highlights the limitations of classical mechanics and the need for more comprehensive theories. It also has practical applications in fields such as astronomy and engineering, where understanding angular momentum is crucial for predicting the behavior of rotating systems.

How is angular momentum measured?

Angular momentum can be measured by multiplying an object's moment of inertia (its resistance to rotational motion) by its angular velocity (the rate at which it rotates). The resulting unit is kilogram meters squared per second (kg·m²/s), which is the standard unit for angular momentum.

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