Hesienberg Uncertanity Principle

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In summary, the video discusses the concept of the commutator and its relationship to uncertainty relations in quantum mechanics.
  • #1
Quarlep
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I watched a video about particle physics and there I saw something strange(for me) (link is here) and there in 13:44 I saw [x,y] I didnt understand because I think uncertanity principle exist only between position and momentum but he make uncertanity between two coordinates .Can somebody explain to me how [x,y] works.

Thanks
 
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  • #2
He explicitly writes

[tex][x,y] = 0[/tex]
[tex][p_x,p_y] = 0[/tex]

So the uncertainty relation for x and y will read

[tex]\Delta x \; \Delta y = 0[/tex]

Then he discusses the commutator for angular momentum.

[tex][L_x,L_y] \neq 0[/tex]

and from that one can derive an uncertainty relation for angular momentum.
 
  • #3
so there's no problem
 
  • #4
no, there isn't
 
  • #5
thanks
 
  • #6
Quarlep said:
I watched a video about particle physics and there I saw something strange(for me) (link is here) and there in 13:44 I saw [x,y] I didnt understand because I think uncertanity principle exist only between position and momentum but he make uncertanity between two coordinates .Can somebody explain to me how [x,y] works.

Thanks


The expression [x, y] is called the commutator of x and y
http://en.wikipedia.org/wiki/Commutator

As you may know it's defined as [x, y] = xy - yx where x and y are any two operators. There's an uncertainty relation for any two observables A and B since [A,B] are what appear in the right hand side and the standard deviations of A and B appear on the left side of the inequality (uncertainty in Q = standard deviation in Q).
 
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  • #7
An uncertainly relation holds between any two non-commuting observables.
 

What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle is a fundamental principle in quantum mechanics that states that the more precisely the position of a particle is known, the less precisely its momentum can be determined, and vice versa. In other words, there is a limit to how accurately we can know both the position and momentum of a particle at the same time.

Who discovered the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle was first proposed by German physicist Werner Heisenberg in 1927. Heisenberg was one of the pioneers of quantum mechanics and the principle is named after him.

What is the significance of the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle has significant implications for the study of quantum mechanics and our understanding of the behavior of particles at the atomic and subatomic level. It also has practical applications in fields such as quantum computing and cryptography.

Can the Heisenberg Uncertainty Principle be violated?

No, the Heisenberg Uncertainty Principle is a fundamental principle of quantum mechanics and has been confirmed by numerous experiments. It is not possible to violate this principle.

How does the Heisenberg Uncertainty Principle affect our daily lives?

While the Heisenberg Uncertainty Principle may seem abstract and only relevant to the study of particles at the subatomic level, it actually has applications in many aspects of our daily lives. For example, it is used in medical imaging techniques, such as MRI, and in the development of new technologies like transistors and lasers.

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