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Vaal
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Given the state and an operator I know the uncertainty of this operator can be calculated via
(see next post latex is being weird, sorry)
(see next post latex is being weird, sorry)
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The scalar is multiplied by the identity operator. Then you can subtract them, and things work out like you'd expect.Vaal said:[tex]\Delta[/tex][tex]\Omega[/tex]2=<[tex]\Psi[/tex]|([tex]\Omega[/tex] - <[tex]\Omega[/tex]>)2|[tex]\Psi[/tex]> (hope that is legible)
but I'm confused as to how the middle, ([tex]\Omega[/tex] -<[tex]\Omega[/tex]>) is defined. Isn't this an operator minus a scalar?
Vaal said:I know I can also find [tex]\Delta[/tex][tex]\Omega[/tex]2 by summing the the products of the probabilities of all the states with the states deviation from the expected value squared, but I thought there was a way to do this without having to know all the probabilities. Thanks.
"Uncertainty of an Operator" refers to the concept in quantum mechanics of how accurately we can know the position and momentum of a particle at the same time.
"Uncertainty of an Operator" is calculated using the Heisenberg Uncertainty Principle, which states that the product of the uncertainty in position and momentum must always be greater than or equal to a specific value known as Planck's constant.
A high uncertainty of an operator value indicates that there is a large range of possible values for the position and momentum of a particle, meaning that our knowledge of its exact location and movement is limited.
The concept of "Uncertainty of an Operator" is closely related to the idea of wave-particle duality in quantum mechanics. This is because the uncertainty principle suggests that a particle cannot have a definite position and momentum at the same time, much like how a wave cannot have a definite wavelength and frequency at the same time.
The uncertainty of an operator cannot be reduced beyond a certain point due to the nature of quantum mechanics. However, by making measurements and observations, we can gain a better understanding of the particle's position and momentum, thus reducing the uncertainty to some extent.