Basic Heisenberg Uncertainty Principle

  • Thread starter the keck
  • Start date
  • #1
22
0

Homework Statement



According the the Uncertainty Principle, an electron of mass m when placed on a 'flat' tabletop will actually 'float' above the table i.e. the vertical position of the electron will be spread out over some distance.

Use the uncertainty principle to find an expression for the equilibrium average height that the electron floats above the table's surface in terms of m,g etc...

Homework Equations



delta(p) x delta (y) >= h/(4*Pi)


The Attempt at a Solution



I used the fact that F=mg=dp/dt and hence delta(p)= mg x delta(t)

Hence delta (y) >= h/(4*Pi*mg*delta(t))

Thus in determining the average height, the delta(t) will cancel, leaving us with :

Average y = h/(4*Pi*mg)

This however seems to be too easy a solution even though unit analysis verifies that it gives us distance.

N.B. I have used both * and x to refer to multiplication

Regards,
The Keck
 

Answers and Replies

  • #3
nrqed
Science Advisor
Homework Helper
Gold Member
3,737
279

Homework Statement



According the the Uncertainty Principle, an electron of mass m when placed on a 'flat' tabletop will actually 'float' above the table i.e. the vertical position of the electron will be spread out over some distance.

Use the uncertainty principle to find an expression for the equilibrium average height that the electron floats above the table's surface in terms of m,g etc...

Homework Equations



delta(p) x delta (y) >= h/(4*Pi)


The Attempt at a Solution



I used the fact that F=mg=dp/dt and hence delta(p)= mg x delta(t)

Hence delta (y) >= h/(4*Pi*mg*delta(t))

Thus in determining the average height, the delta(t) will cancel, leaving us with :

Average y = h/(4*Pi*mg)
How did you get that?:confused:
This does not have the dimensions of a distance.

The steps before that last equation were ok, I don't see how you got this last expression.

PS: welcome to the forums!
 
  • #4
Dick
Science Advisor
Homework Helper
26,260
619
Yeah, I don't follow the logic at all. I'm used to problems like this being treated as energy minimization problems. Ie minimize kinetic plus potential energy:

p^2/(2m)+mgy

subject to the constraint py>=h/(4*pi). This doesn't seem to be the same thing...
 
  • #5
22
0
Yeah...Sorry about that guys, I had a look at the dimensional analysis again, and realised that it doesn't match.

So how do I actually do it? I'm not exactly sure how one determines the average equilibrium average position.

Thanks

Regards.
The Keck
 
  • #6
Dick
Science Advisor
Homework Helper
26,260
619
I already pointed this out, but minimize p^2/(2*m)+mgy subject to the constraint of the uncertainty principle (where p and y are 'average equilibrium' values and ought to be roughly the same as [tex]\Delta x[/tex] and [tex]\Delta p[/tex]). Don't worry about being terribly exact about defining things like 'average equilibrium' - this is an estimate, not an exact calculation.
 
Last edited:
  • #7
1
0
who the hell are u guys?

r u guys university students or school students ?
im just worried . . im preparing for one of the toughest exams in the world and couldnt solve that one . . . https://www.physicsforums.com/images/smilies/surprised.gif [Broken]
:surprised
 
Last edited by a moderator:
  • #8
Dick
Science Advisor
Homework Helper
26,260
619
r u guys university students or school students ?
im just worried . . im preparing for one of the toughest exams in the world and couldnt solve that one . . . https://www.physicsforums.com/images/smilies/surprised.gif [Broken]
:surprised
I suspect everybody who posts here may give you a different answer.
 
Last edited by a moderator:
  • #9
22
0
Indeed, there are a variety of ways to obtain the answer. The answer one gets will vary by 0.1-0.5 mm, but as long as the unit analysis is correct, then I doubt they can really mark you down...if you provide valid reasoning.

Dick's method is the one I used, and is quite valid. Thanks a lot!!!

Regards,
The Keck
 
  • #10
From the uncertainty principle you can write
(delta y)*(delta p)~hbar/2
You can also write (delta p)~squire root{2m(delta E)}
You can also put (delta E)~mg(delta y)
From these relations you can have

(delta y)~((hbar)^{2/3})/(2m^{2/3} g^{1/3})

Shyamal Biswas
 

Related Threads on Basic Heisenberg Uncertainty Principle

  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
0
Views
2K
Replies
3
Views
4K
Replies
0
Views
6K
Replies
1
Views
2K
Replies
1
Views
2K
Replies
4
Views
2K
Replies
14
Views
42K
Replies
1
Views
3K
Top