Heisenberg Uncertainty principle in 3D

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SUMMARY

The discussion centers on applying the Heisenberg Uncertainty Principle to calculate the minimum volume in which a positron is located based on its measured velocities. The user correctly identifies the formula Δx=hbar/(2*m*Δvx) for calculating uncertainty in position but fails to incorporate the velocity values into the calculations. The user initially computes a volume of V=1.12*10-25 m³, while the correct answer is V=1.4*10-26 m³, attributed to an error in the reference material rather than a miscalculation.

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  • Understanding of the Heisenberg Uncertainty Principle
  • Familiarity with basic quantum mechanics concepts
  • Knowledge of relativistic and non-relativistic physics
  • Proficiency in using physical constants such as hbar and mass
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  • Study the derivation and implications of the Heisenberg Uncertainty Principle
  • Learn how to apply relativistic equations in quantum mechanics
  • Explore the significance of velocity measurements in uncertainty calculations
  • Investigate common errors in quantum mechanics textbooks and their resolutions
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Students of quantum mechanics, physicists working with particle physics, and educators teaching the Heisenberg Uncertainty Principle.

mat8845
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Hi there,

So here's my assignment:

''The velocity of a positron is measured to be: vx=(4.00±0.18)*105 m/s, vy=(0.34±0.12)*105 m/s, vz=(1.41±0.08)*105 m/s. Within what minimum volume was the positron located at the moment the measurement was carried out?''

I think I'm not wrong when I say that the uncertainty principle applies in every direction. Since the velocities are not relativistic, the simple equation should be:

Δx=hbar/(2*m*Δvx)

The same equation is used for Δy and Δz, and we only take the volume of the ''uncertainty box'' V=ΔxΔyΔz.

With the positron having a mass of 9.109*10-31kg, that gives me V=1.12*10-25 m3. But I know the right answer is 1.4*10-26 m3.

Even with the relativistic equations, I get the same wrong answer.

So what am I doing wrong? Note that I never used the values of the velocities. Should I use them somewhere?

Thank you for your time.
 
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Nevermind, there was a mistake in the book.
 

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