Question about uncertainty princple?

In summary, the uncertainty principle states that for a particle with measured z-component of angular momentum, the x and y components cannot be known for certain. This means it is impossible to say that the total angular momentum of the particle is zero, as the other components could have non-zero values. However, this does not violate the uncertainty principle. For example, in the case of S-orbitals in a hydrogen atom, all components can be measured to be zero simultaneously. To measure the angular momentum of an S orbital, one could use the Stern-Gerlach experiment. In regards to the potential energy of two charged particles at different distances, it is impossible to determine the exact value without doing the necessary calculations.
  • #1
cragar
2,552
3
Lets say I measure the z-component of a particles angular momentum, then I can't know for certain the x and y componets. So if I measure the Z componet to be 0, the x and y componets could be zero or not.
So is it impossible to say that the particles total angular mometum is zero meaning all the componets are zero. Would this violate the uncertainty principle?
 
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  • #2
cragar said:
Lets say I measure the z-component of a particles angular momentum, then I can't know for certain the x and y componets. So if I measure the Z componet to be 0, the x and y componets could be zero or not.
So is it impossible to say that the particles total angular mometum is zero meaning all the componets are zero. Would this violate the uncertainty principle?

No, as you do not know what the values are. That is what the principle means. They COULD be zero, or they might not be.
 
  • #3
so i could measure one of the components at it could be zero but I won't know what the other components are .
 
  • #4
I have a question that has to do with HUP ---- at least i suppose.
Let say we have two unity electric charge far way from each other in a distance D= 3.481*10^7 They are in static position. THe potential energy of them is E = e^2 / D *eps.0 = h/1 erg.
Let suppose that will have another distance D1 = D+1 cm. I am in dilema to know how will be the potential energy: < h/1 or 0?
 
  • #5
So is it impossible to say that the particles total angular mometum is zero meaning all the componets are zero. Would this violate the uncertainty principle?

No, that's not true; measuring precisely 0 total angular momentum does not violate the uncertainty principle. For example, the S-orbitals in a hydrogen atom have exactly 0 angular momentum. This is allowed because the commutators for angular momentum have the "strange" form,

[tex]
[L_x, L_y] = i\hbar L_z
[/tex]
[tex]
[L_y, L_z] = i \hbar L_x
[/tex]
[tex]
[L_z, L_x] = i \hbar L_y
[/tex]

And as you know, the uncertainty principle between two operators depends on the commutator:

[tex]
\Delta A \Delta B = \frac{1}{2} |[A, B]|
[/tex]

So if all components are zero, they all can be measured simultaneously.

For nonzero L, by contrast, L2 and Lz can be measured simultaneously, and from there you can deduce how much of the rest is distributed among Lx and Ly, but it is impossible to go further and resolve the two individual components.
 
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  • #6
ok thanks for you answer mike . And how do we measure the angular momentum of the S orbital in the hydrogen atom? Would we just do the Stern–Gerlach experiment?
 
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  • #7
mquirce said:
I have a question that has to do with HUP ---- at least i suppose.
Let say we have two unity electric charge far way from each other in a distance D= 3.481*10^7 They are in static position. THe potential energy of them is E = e^2 / D *eps.0 = h/1 erg.
Let suppose that will have another distance D1 = D+1 cm. I am in dilema to know how will be the potential energy: < h/1 or 0?

Did you do the math with the new distance? What is the new value?
 

1. What is the uncertainty principle?

The uncertainty principle, also known as Heisenberg's uncertainty principle, is a fundamental concept in quantum mechanics that states that it is impossible to know with certainty both the position and momentum of a particle at the same time. In other words, the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

2. Who discovered the uncertainty principle?

The uncertainty principle was first proposed by German physicist Werner Heisenberg in 1927. Heisenberg's work on the uncertainty principle was a key development in the field of quantum mechanics and revolutionized our understanding of the atomic and subatomic world.

3. What is the mathematical expression of the uncertainty principle?

The mathematical expression of the uncertainty principle is ΔxΔp ≥ ħ/2, where Δx represents the uncertainty in position, Δp represents the uncertainty in momentum, and ħ is the reduced Planck's constant. This expression shows that the product of the uncertainties in position and momentum cannot be less than a certain value, confirming the principle that it is impossible to know both with certainty simultaneously.

4. How does the uncertainty principle impact our understanding of the physical world?

The uncertainty principle has significant implications for our understanding of the physical world. It challenges the classical notion of determinism, which states that the behavior of particles can be predicted with complete accuracy. Instead, it introduces the concept of inherent uncertainty and indeterminacy at the subatomic level, highlighting the probabilistic nature of quantum mechanics.

5. Can the uncertainty principle be violated or overcome?

No, the uncertainty principle is a fundamental aspect of quantum mechanics and cannot be violated or overcome. It is a fundamental limitation on our ability to measure and predict the behavior of particles at the subatomic level. However, advancements in technology and techniques have allowed scientists to make more precise measurements, minimizing the effects of uncertainty in certain cases.

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