Expectation Value of Angular Momentum

In summary, in the ground-state of the 2D rigid rotor, the expectation value for the angular momentum is zero and the corresponding uncertainty is also zero. The uncertainty in position can be described as the range of possible positions for a particle within a given level of uncertainty. The rigid rotor can have a vanishing zero-point energy and still be consistent with the uncertainty relation because the uncertainty relation only applies to individual measurements, not the average energy of a system.
  • #1
jgens
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Homework Statement



1. For the ground-state of the 2D rigid rotor what is the expectation value of the angular momentum? And what is the corresponding uncertainty in this value?

2. Describe in words what the uncertainty in position is.

3. Explain why the rigid rotor can have vanishing zero-point energy and still be consistent with the uncertainty relation.

Homework Equations



N/A

The Attempt at a Solution



So, right now I am just stuck on part 1. The spherical harmonic for the ground-state is just a constant, which makes me believe the expectation value for the angular momentum should be zero. Can anyone confirm if this is correct?
 
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  • #2
And since the expectation value is zero, does that mean the corresponding uncertainty is also zero? Thanks in advance.
 

What is the Expectation Value of Angular Momentum?

The expectation value of angular momentum is a measure of the average or most probable value of the angular momentum of a system in quantum mechanics. It is calculated by taking the inner product of the angular momentum operator and the wavefunction of the system.

How is the Expectation Value of Angular Momentum calculated?

The expectation value of angular momentum is calculated by taking the inner product of the angular momentum operator and the wavefunction of the system. This is represented mathematically as Lexp = ψ|L|ψ, where L is the angular momentum operator and ψ is the wavefunction.

What is the physical significance of the Expectation Value of Angular Momentum?

The expectation value of angular momentum has physical significance as it represents the average or most probable value of the angular momentum of a system. It is used to predict the behavior of particles in quantum mechanics and can also be used to determine the orientation of an electron's spin.

How does the Expectation Value of Angular Momentum relate to the Uncertainty Principle?

The expectation value of angular momentum is related to the uncertainty principle, which states that the more precisely the angular momentum of a particle is known, the less precisely its position can be known, and vice versa. This means that knowing the expectation value of angular momentum can provide information about the uncertainty in the position of a particle.

Can the Expectation Value of Angular Momentum be experimentally measured?

Yes, the expectation value of angular momentum can be experimentally measured. This can be done by performing experiments that measure the angular momentum of a system and then calculating the expectation value using the measured data. However, due to the uncertainty principle, the measurement will have some degree of uncertainty.

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