Easy QM uncertainty question

[quasar987]

The setting is the following: Mr. Leonelli lives in quantumland where h = 100 [Js]. His mass is m = 80 kg, his speed is v = 1.1 m/s. Can Mr. Leonelli rest in his seat?

We're confused about the meaning of the uncertainty relation, in light of the fact that we're told that his speed is 1.1 and his mass is 80. So his momentum is 88. Right there, without even considering quantum effects, we can tell that he cannot be AT REST in his seat.

On the other hand, we understand that if we know him to be in his seat, then $\Delta x = 0$, so $\Delta p = \infty$, but we believe that this does not mean that the uncertainty on p IN THE SENSE OF classical laboratory data is infinite. We think it only means that his momentum is undefined, or rather, spread out over an infinite margin, such that for a given measure on it, it can be anything. Again, this would contradict the fact that the setting of the problem states p=88.

Any thruth in those words or are we off track?

 

[lightgrav]

My chair is about .5m wide; I'd say I was
"in my seat" if I had Delta_x < .5m

More to the point, I think that the use of "speed"
rather than "velocity" tips you off that
this is not intended as an average velocity
(which could be zero RELATIVE to his chair),
but as a width of the speed distribution
(which implies a width in momentum-space).

The big picture:
wean yourself from expecting precisely-known locations.

 

[quasar987]

So you're suggesting that v = 1.1 refers to the width of the velocity? That'd be nice and everything would be clear... but why would he ask in question (a) "What is the wavelenght of Mr. Leonelli" instead of "what is the range of wavelenght making up Mr. Leonelli's wave function"?

Also, do you really think that the teacher expects us to arbitrarily set a value of the width of the chair and get different answers with every student while he could have said the chair has width 0.5m and save himself the trouble?

Also, couldn't we assume Mr. Leonelli himself to have a width, such that when he sits in his chair, he fits perfectly, and hence $\Delta x = 0$?

P.S. I forgot to mention that Mr. Leonelli is in a square room 5m x 5m with two doors on one wall (which I guess are assumed to be closed in the context of question (b) "Can Mr. Leonelli rest in his seat?")

 

[quasar987]

Also, couldn't we assume Mr. Leonelli himself to have a width, such that when he sits in his chair, he fits perfectly, and hence $\Delta x = 0$?

Edit: I retract this part and change it to: "Since the teacher didn't specify a width for the chair, could it be that it is because he wanted us to assume, somewhat artificially, that when Leonelli is in his chair, it means $\Delta x = 0$."
In other words, it was a hint that Leonelli's chair is to be considered as a point.
I mean, classically, if he's in his chair, he's in his chair and he's nowhere else, so his position is well defined / peaked about the position of his "punctual chair". If Leonelli was a point particle, then his chair would be a point too and the statement "leonelli in his chair" would be equivalent to "Leonelli's wave function is $\delta(x-x_{chair}) \Rightarrow \Delta x = 0$". Ok, I'll stop babling now.

Tell me what you think lightgrav (others are welcome to bump-in too ).

 

[lightgrav]

I had thought
that the author expected you to compute
a minimum chair width (from the inequality)
that's so small, folks who compute it correctly agree
that anything smaller wouldn't be a "seat".

The author asked what his wavelength was
so you'd have a wavelength to compare with 5m.
He can't fit in the room but he can stay "on" a chair.
That's too cool of a situation to pass up.

If Mr. Leonelli had a width (in location), then
Delta_x is not zero!

Do you know the distance between the doors?
(is he able to leave through both of them?)

 

[quasar987]

I had thought
that the author expected you to compute
a minimum chair width (from the inequality)

what inequality?

If Mr. Leonelli had a width (in location), then
Delta_x is not zero!

yeah, I retracted that part.

Do you know the distance between the doors?
(is he able to leave through both of them?)

yeah, 2m. And they are both 0.70m wide. But the doors are probably only related to questions (c) and (d) (which are as vague and obscure and (a) and (b) I'm afraid )

 

[lightgrav]

the uncertainty relation is an INequality.
What do you get for the required size of this "seat"?

So part (c) asks about his transverse spread
as he tries to leave thru one door only,
and part (d) asks about his transverse spread
(or is it 2-path interference) thru both doors.