What is L^2Ψ for a 3px state of a H-atom?

In summary, the conversation is about a homework problem involving an H-atom in a 3px state and the measurement of its total orbital angular momentum. There is some confusion about which wavefunction to use and whether to use the expectation value or do the integral. It is suggested that the average value for 100 measurements of the 3px state would be 0. There is also a discussion about the eigenvalues of L^2 and the relationship between it and H.
  • #1
mordacious
2
0
Awesome forum here!

I'm stuck on a homework problem and need some guidance.

A H-atom exists in a 3px state. What would be the result of measuring the total orbital angular momentum of this state (e.g. 100 measurements)?

I assume when they say 100 measurements that they mean the expectation value? If so there is now the problem of which wavefunction to use as a 3px state has three due to m = -1, 0, +1. I remember something about how orbitals in the same subshell can be combined but I can't find it in my notes and I'm not sure if this is what I'm looking for.

Anyways, even if I just choose one randomly, finding ∫Ψ*L^2Ψdτ is a huge task.

Am I just going about this all wrong?

Thanks,
Ashley
 
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  • #2
What is a 3px state ? What quantum numbers does it have ?
 
  • #3
dextercioby said:
What is a 3px state ? What quantum numbers does it have ?

n = 3
l = 1
m = -1, 0, +1

I'm starting to think this is more of a thinking question than a calculation question. If 3p-1 and 3p+1 give one value and 3p0 gives 0 then over 100 measurements the average value would be 0. Does this sound logical?

Ashley
 
  • #4
As far as i know, the p_x orbital has a definite value of "m_l". So your last answer is wrong.
 
  • #5
It wouldn't matter if the eigenvalues of L^2 don't depend on m. So do they?

Doing the integral looks like a fun exercise, but it's not necessary. What is L^2Ψ? (Hint: H and L^2 commute for the H-atom).
 

1. What is Orbital Angular Momentum?

Orbital Angular Momentum (OAM) is a physical quantity that describes the rotation of a particle or system of particles around an axis. It is a type of angular momentum that is associated with the motion of an object in a circular or elliptical orbit.

2. How is Orbital Angular Momentum calculated?

The magnitude of OAM is calculated by multiplying the orbital radius of the particle by its linear momentum and the sine of the angle between the linear momentum vector and the axis of rotation. The direction of OAM is perpendicular to both the orbital plane and the axis of rotation.

3. What is the significance of Orbital Angular Momentum in physics?

OAM is an important concept in physics, particularly in quantum mechanics. It is used to describe the rotational motion of particles, such as electrons, around the nucleus of an atom. It also plays a role in the study of angular momentum conservation and the behavior of rotating systems.

4. How is Orbital Angular Momentum related to Spin Angular Momentum?

Spin Angular Momentum is a type of intrinsic angular momentum that is associated with the spin of a particle. Orbital Angular Momentum, on the other hand, is related to the motion of the particle around an axis. Both types of angular momentum can exist simultaneously and contribute to the total angular momentum of a system.

5. Can Orbital Angular Momentum be observed or measured?

Yes, Orbital Angular Momentum can be observed and measured using various experimental techniques. In quantum mechanics, it is quantized, meaning it can only take on discrete values. In classical mechanics, it can take on any value depending on the orbital motion of the particle. Scientists use tools such as particle accelerators and spectroscopy to study and measure the OAM of particles.

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