Heisenberg's Momentum-Position Uncertainty Principle

In summary, Heisenberg discovered that it is impossible to determine both the position and momentum of a particle with unlimited precision at the same time. This is represented by the equation \Delta p\Delta x \geqh/2, where h is Planck's constant over 2pi. This is due to the concept of large wavenumbers and the uncertainty principle in quantum mechanics. This is similar to the idea of Fourier transforms, where knowing the frequency of a sine wave requires giving up localization in time. In the quantum world, this means sacrificing the ability to measure both the position and momentum of a particle with absolute precision.
  • #1
Koshi
18
0
I was reading about how Heisenberg found out that it is "impossible to determine simultaneously with unlimited precision the position and momentum of a particle" (Serway/Moss/Moyer, 174)

[tex]\Delta p\Delta x \geq[/tex][STRIKE]h[/STRIKE]/2 (where [STRIKE]h[/STRIKE] is plank's constant over 2pi.)

My question is why is this true? I read that it had something to do with the large wavenumbers [tex]\Delta[/tex]k, but I'm unsure exactly how that affects anything. I'm just a little hazy on the reason for why, even ignoring the error caused by measuring insturments, it would be impossible to measure two precise things at once.
 
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  • #2
One way of gaining some intuition is to consider Fourier transforms. It is impossible to exactly know the frequency of a sine wave unless you have an infinitely long interval to measure it. To know its frequency (energy) you give up all localization in time. The same holds in the quantum world.
 

1. What is Heisenberg's Momentum-Position Uncertainty Principle?

Heisenberg's Momentum-Position Uncertainty Principle is a fundamental principle in quantum mechanics that states that it is impossible to know both the exact momentum and position of a particle at the same time.

2. Who discovered the Momentum-Position Uncertainty Principle?

The Momentum-Position Uncertainty Principle was first proposed by Werner Heisenberg in 1927 as part of his uncertainty principle, which describes the limitations of measuring certain properties of particles in quantum mechanics.

3. What is the mathematical formula for Heisenberg's Momentum-Position Uncertainty Principle?

The mathematical formula for Heisenberg's Momentum-Position Uncertainty Principle is ΔpΔx ≥ h/4π, where Δp represents the uncertainty in momentum, Δx represents the uncertainty in position, and h is the Planck constant.

4. How does Heisenberg's Momentum-Position Uncertainty Principle impact our understanding of the behavior of particles?

Heisenberg's Momentum-Position Uncertainty Principle tells us that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This means that at the quantum level, particles do not have definite properties, but rather exist in a state of uncertainty.

5. Can Heisenberg's Momentum-Position Uncertainty Principle be violated?

No, Heisenberg's Momentum-Position Uncertainty Principle is a fundamental principle in quantum mechanics and has been experimentally verified numerous times. It is a fundamental part of our understanding of the behavior of particles at the quantum level.

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