Heisenberg Uncertainty principle in 3D

In summary, the conversation discusses an assignment which involves measuring the velocity of a positron and determining the minimum volume in which it was located. The uncertainty principle is mentioned and a simple equation is used to calculate the volume, but the correct answer differs from the one given in the book. The conversation ends with the person asking for help in figuring out their mistake.
  • #1
mat8845
3
0
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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  • #2
Nevermind, there was a mistake in the book.
 

1. What is the Heisenberg Uncertainty Principle in 3D?

The Heisenberg Uncertainty Principle is a fundamental concept in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle in 3D space. This means that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

2. How does the Heisenberg Uncertainty Principle apply in 3D?

The Heisenberg Uncertainty Principle applies in 3D in the same way as it does in 1D or 2D. It is a fundamental principle of quantum mechanics that applies to all objects and particles in 3D space.

3. What are the implications of the Heisenberg Uncertainty Principle in 3D?

The Heisenberg Uncertainty Principle has many implications in 3D. It means that there are inherent uncertainties in the measurements we make of particles in 3D space, and that there is a fundamental limit to the precision with which we can know the properties of a particle.

4. How does the Heisenberg Uncertainty Principle affect our understanding of the physical world in 3D?

The Heisenberg Uncertainty Principle has had a profound impact on our understanding of the physical world in 3D. It has forced us to accept that there are inherent uncertainties in the measurements we make, and that our understanding of the physical world is limited by our ability to observe it.

5. Are there any exceptions to the Heisenberg Uncertainty Principle in 3D?

The Heisenberg Uncertainty Principle is a fundamental principle of quantum mechanics and applies to all particles in 3D space. However, there are certain situations where it may not apply, such as in macroscopic objects or in systems that are not in a pure quantum state. However, in general, the Heisenberg Uncertainty Principle applies to all particles in 3D space.

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