Can you find two different constants by Noether's theorem

In summary, the conversation discusses a problem from Classical Dynamics: A contemporary approach by Jose, which involves finding symmetric transformations for a 3-dimensional one-particle system with a potential energy in cylindrical polar coordinates. One solution has already been found, but the student is struggling to find another one. Another person suggests considering symmetries in time to find the second solution.
  • #1
qinglong.1397
108
1

Homework Statement



Consider a 3-dimensional one-particle system whose potential energy in cylindrical polar coordinates [tex]\rho[/tex], [tex]\theta[/tex], z is of the form V([tex]\rho[/tex], k[tex]\theta[/tex]+z), where k is a constant.

Homework Equations


The Attempt at a Solution



I already find a symmetric transformation:
[tex]\rho '[/tex]=[tex]\rho[/tex], [tex]\theta '[/tex]=[tex]\theta[/tex]+[tex]\theta_0[/tex], z'=z-k[tex]\theta_0[/tex].

Can you help me find at least another one? Thank you!
 
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  • #2
No body can do it?
 
  • #3
For starters, are you sure there is another one?
 
  • #4
And what have you done on the problem? It is strictly against policy to just hand out answers -- it's cheating and does little to help the student learn.
 
  • #5
Hurkyl said:
And what have you done on the problem? It is strictly against policy to just hand out answers -- it's cheating and does little to help the student learn.

I found one solution, as mentioned in the first post. I just do not know how to find the other one. I need your help. Just hint. Thanks!
 
  • #6
This is a problem from Classical Dynamics: A contemproray approach by Jose. I think it is not very possible that it is wrong.
 
  • #7
Ah yes... problem 3.11 by any chance? Now that you mention it, I remember doing that one for a homework assignment once upon a time :wink: and I seem to remember having the same difficulty with it.

Try thinking about symmetries in time, since you've already considered the three spatial coordinates.
 
  • #8
diazona said:
Ah yes... problem 3.11 by any chance? Now that you mention it, I remember doing that one for a homework assignment once upon a time :wink: and I seem to remember having the same difficulty with it.

Try thinking about symmetries in time, since you've already considered the three spatial coordinates.

Oh, yeah. I never thought about that. Thank you very much!
 

FAQ: Can you find two different constants by Noether's theorem

What is Noether's theorem?

Noether's theorem is a fundamental principle in physics that states that for every symmetry in a physical system, there exists a corresponding conservation law. It was proposed by mathematician Emmy Noether in 1915 and has been widely used in various fields of physics, including classical mechanics, electromagnetism, and quantum mechanics.

How does Noether's theorem relate to constants?

Noether's theorem can be used to find conserved quantities in a physical system. These conserved quantities are often referred to as constants, as their values do not change over time. This relationship between Noether's theorem and constants allows us to understand the underlying symmetries and laws that govern a physical system.

Can you find two different constants using Noether's theorem?

Yes, it is possible to find multiple constants using Noether's theorem. This is because there can be multiple symmetries present in a physical system, and each symmetry corresponds to a different conserved quantity or constant. The number of constants that can be found using Noether's theorem depends on the complexity of the system and the number of symmetries present.

What is the significance of finding constants using Noether's theorem?

Finding constants using Noether's theorem is significant because it allows us to better understand the underlying laws and symmetries of a physical system. It also helps us make predictions and calculations about the behavior of the system. Additionally, constants found using Noether's theorem can be used to verify the accuracy of a physical theory.

Are the constants found by Noether's theorem always exact?

No, the constants found by Noether's theorem are not always exact. In some cases, they may only be approximate or valid under certain conditions. This is because Noether's theorem is a theoretical framework that is dependent on the assumptions and approximations made in a given physical system. However, the constants found using Noether's theorem are often very close approximations and can still be extremely useful in understanding and predicting the behavior of a system.

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