Uncertainty principle

In summary, The Heisenberg Uncertainty principle states that the product of the uncertainties in position and momentum must be greater than or equal to Planck's constant divided by 2 times pi. However, there is another expression, where the product must be greater than or equal to Planck's constant divided by 4 times pi. When asked which expression to use in competitive exams, the lecturer suggested using the second one, as it is the form given in modern textbooks. In 1D, the lower bound for the product of uncertainties is the second expression.
  • #1
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Homework Statement


According to Heisenberg Uncertainty principle,
Del(X)xdel(P) >= h/2(pi)
But there is also another expression given in my book which is,
Del(X)xdel(P) >= h/4(pi)
I asked my lecturer why is it so? She said that, the second expression is obtained from Fourier analysis. But she also said that in calculations, you can use the first one. Which should I use in competitive exams?



Homework Equations





The Attempt at a Solution

 
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  • #2
The second one is the form given in all modern textbooks and the one you will be expected to use in your exams.
 
  • #3
In 1D I believe the lower bound on the product of these uncertainties is your second expression.
 

What is the uncertainty principle?

The uncertainty principle, also known as Heisenberg's uncertainty principle, is a fundamental principle in quantum mechanics that states that it is impossible to know both the precise position and momentum of a particle at the same time.

Who discovered the uncertainty principle?

The uncertainty principle was first proposed by German physicist Werner Heisenberg in 1927.

How does the uncertainty principle affect our understanding of the physical world?

The uncertainty principle challenges our classical understanding of the physical world, as it shows that at the subatomic level, particles do not behave in a predictable manner. It also has implications for the accuracy of measurements and the limitations of scientific knowledge.

What is the mathematical equation for the uncertainty principle?

The mathematical equation for the uncertainty principle is ΔxΔp ≥ ħ/2, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and ħ is the reduced Planck's constant.

How is the uncertainty principle related to the concept of wave-particle duality?

The uncertainty principle is closely related to the concept of wave-particle duality, which states that particles can exhibit both wave-like and particle-like behavior. The uncertainty principle arises because it is impossible to determine the position of a particle without disturbing its momentum, and vice versa, due to the wave-like nature of particles at the quantum level.

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