Problems about uncertainty principle

[athrun200]

It seems the book makes a mistake.
Uncertainty principle states: (Uncertainty of p) times (uncertainty of x)>=(a constant)
But in the following picture, the writer calculates the exact value of momentum and find uncertainty of x. Is it wrong?

I am using Understanding Physics written by Michael Mansfield & Colm O'Sullivan
[PLAIN]http://a367.yahoofs.com/hkblog/LR5wVsiTBB9XH4KDYpBfXDI-_9/blog/20110510041944520.jpg?ib_____DTLgSu0Su

 

[Demystifier]

It is wrong, but not completely. Namely, in the first case, Delta p is certainly much smaller than the average p itself, so the actual Delta x is much larger than estimated.

In the second case, it is not unreasonable to assume that Delta p is of the same order of magnitude as the average p itself, so the second estimate is somewhat better.

 

[BruceW]

The writer is using the exact value of momentum as an estimate on the spread of momentum values.
Textbooks often do this, and its not an exact method, but it often gives an approximately correct answer.

 

[lepton5]

I think the uncertainty principle says: in microscopic world(about atomic radius); if an observer try to calculate/find an exact value of particle's momentum then the exact location of its particle will become uncertain (its location will spread in statistical distribution), vice versa

So, I think what the author try to explain is : if you can calculate particle's momentum in great precision, then you will get uncertain for its location, and vice versa.

In macroscopic world, the uncertainty principle can be ignored (we don't experience it) but not in atomic level. because in atomic level if we want to measure the momentum of particle, we will disturb its location. more precise you measure (momentum) more great disturbance is (location)

so, there is nothing wrong with your textbook...^-^

 

[BruceW]

Lepton5, you're not quite right. You can precisely measure momentum and position, you just can't predict what those values will be before you make the measurement. This is a common misconception.

 

[256bits]

Uncertainty principle states: (Uncertainty of p) times (uncertainty of x)>=(a constant)

Notice the "greater than or equal to" inequality.
The uncertainty can never be less than this value.
So your "a"*is not necessarily a constant, but is a value of which the uncertainty cannot be less than, but can be equal to or greater than.

 

[lepton5]

Lepton5, you're not quite right. You can precisely measure momentum and position, you just can't predict what those values will be before you make the measurement. This is a common misconception.

Of course, particles has its momentum and where its location (exactly before we measure it). but the problem is in the atomic world, we cannot measure two quantity like momentum and position, in precisely altogether, just like i said above. measurement itself can disturb the state of particle.

 

[SeanGillespie]

Will someone please explain why my textbooks/lectures have taught me that the uncertainty principle is (delta x)(delta p) = (h-bar).
While wikipedia states that (delta x)(delta p) >= (h-bar)/2.

 

[SpectraCat]

Of course, particles has its momentum and where its location (exactly before we measure it). but the problem is in the atomic world, we cannot measure two quantity like momentum and position, in precisely altogether, just like i said above. measurement itself can disturb the state of particle.

No .. both parts of that are wrong in terms of standard quantum mechanics.

1) particles do not have well-defined positions and momenta prior to measurement

2) the HUP is not a measurement problem .. the uncertainties in position and momentum are intrinsic to the quantum state of the particle .. this is because position and momentum are non-commuting operators in quantum mechanics.

 

[SpectraCat]

Will someone please explain why my textbooks/lectures have taught me that the uncertainty principle is (delta x)(delta p) = (h-bar).
While wikipedia states that (delta x)(delta p) >= (h-bar)/2.

If your textbooks said that then they are (at best) imprecise. That relation (with equality) can be correct in certain special circumstances (the ground state of the harmonic oscillator for instance), but in general it is the inequality which holds.

 

[lepton5]

No .. both parts of that are wrong in terms of standard quantum mechanics.

1) particles do not have well-defined positions and momenta prior to measurement

2) the HUP is not a measurement problem .. the uncertainties in position and momentum are intrinsic to the quantum state of the particle .. this is because position and momentum are non-commuting operators in quantum mechanics.

you can discuss about HUP in many way. what I've said about HUP here is just basic idea HUP as discussed in many textbook (check : Hewitt conceptual physics & Wheeler Quantum Theory and Measurement). and i think it can be understood even for layman physics.

I think i can safely agree with u (point 1), even particles existence is questionable prior to measurement (many physicist has long debate about this, it's simply my believe i said above. well it maybe wrong).

and, i guess you approach HUP in mathematical way and i think its very abstract way if we want explain HUP to layman. i relate HUP in measurement to simplify it, as many textbook do it. (i think the first idea HUP is related to measurement in atomic level).

for ending, i quote from Feynman : "I think i can safely say that nobody understands quantum mechanics (completely)". ^-^

 

[Matterwave]

If your textbooks said that then they are (at best) imprecise. That relation (with equality) can be correct in certain special circumstances (the ground state of the harmonic oscillator for instance), but in general it is the inequality which holds.

Actually the ground state of the QHM reaches the quantum limit of hbar/2 (rather than hbar). The equality with hbar is like some sort of rough estimate or something...

 

[athrun200]

In fact, I've homework about HUP.
https://www.physicsforums.com/showthread.php?t=497803

If you are interested in it, please help me.

 

[SpectraCat]

Actually the ground state of the QHM reaches the quantum limit of hbar/2 (rather than hbar). The equality with hbar is like some sort of rough estimate or something...

Hehe .. whoops! Missed the fact that the factor of 1/2 was missing on the RHS of the first equation.

 

[DrChinese]

I think i can safely agree with u (point 1), even particles existence is questionable prior to measurement (many physicist has long debate about this, it's simply my believe i said above. well it maybe wrong).

That wasn't what was said. As far as anyone knows, a particle's conserved quantities remain constant. Total energy, charge, etc. So the particle is not considered to cease to exist in this regard when not observed.