Why Are There Two Different Expressions for Uncertainty in Quantum Mechanics?

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SUMMARY

The discussion centers on the two expressions for the Heisenberg Uncertainty Principle in quantum mechanics: Del(X) x Del(P) ≥ h/2π and Del(X) x Del(P) ≥ h/4π. The latter expression, derived from Fourier analysis, is the standard form found in modern textbooks and is the one recommended for use in competitive exams. The first expression can be used for calculations, but the second is preferred for theoretical understanding and exam preparation.

PREREQUISITES
  • Understanding of the Heisenberg Uncertainty Principle
  • Familiarity with Fourier analysis
  • Basic knowledge of quantum mechanics
  • Ability to perform calculations involving physical constants
NEXT STEPS
  • Study the derivation of the Heisenberg Uncertainty Principle using Fourier analysis
  • Explore the implications of the uncertainty principle in quantum mechanics
  • Review modern textbooks on quantum mechanics for updated expressions
  • Practice problems involving the application of the uncertainty principle in competitive exams
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Students of quantum mechanics, physics educators, and individuals preparing for competitive exams in physics will benefit from this discussion.

Amith2006
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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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The second one is the form given in all modern textbooks and the one you will be expected to use in your exams.
 
In 1D I believe the lower bound on the product of these uncertainties is your second expression.
 

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