Uncertainty relation derivation

In summary, the lecturer introduced the concept of commutation between two operators and stated that if they commute, they can be simultaneously measured. However, if they do not commute, they cannot be measured simultaneously. Additionally, the lecturer explained that if the operators cannot commute, there is an uncertainty relation between their values. Finally, a question was raised about measuring the y momentum of an object and whether it allows for measuring the x and z positions, to which the lecturer provided a resource for further understanding.
  • #1
Somali_Physicist
117
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Hey guys , my lecturer introduced a new concept with reference to the commutation of two operators.He claimed that if two commutators commute then they can be simultaneously measured.I can clearly see how this works.He then went on and state if they don't commute they can't simultaneously be measured.However he went further and claimed if they cannot commute then the uncertainty relation between the operators values is:

2ΔqΔs ≥ abs(<[Q^,S^]>)

Does anyone have a derivation for this bizaare relation.

Finally , if we measure the y momentum of an object , can we also meausre the x and z position?
 
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FAQ: Uncertainty relation derivation

What is the uncertainty relation derivation?

The uncertainty relation derivation is a mathematical proof that describes the relationship between the uncertainties in position and momentum of a particle. It was first proposed by Werner Heisenberg in 1927 as part of his uncertainty principle.

Why is the uncertainty relation important?

The uncertainty relation is important because it sets a fundamental limit on the precision with which certain pairs of physical properties can be measured. It has significant implications in quantum mechanics and has been confirmed by numerous experiments.

How is the uncertainty relation derived?

The uncertainty relation is derived using mathematical equations and principles from quantum mechanics. It involves calculating the variances of position and momentum operators and applying the Cauchy-Schwarz inequality to these variances.

Are there any exceptions to the uncertainty relation?

No, the uncertainty relation is a fundamental principle in quantum mechanics and applies to all systems and particles. There are no known exceptions to this relation.

Can the uncertainty relation be violated?

No, the uncertainty relation is a mathematical consequence of the fundamental principles of quantum mechanics and cannot be violated. Any apparent violation of the uncertainty relation is due to experimental limitations or errors in measurement.

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