Uncertainty principle - just want to check my method

  • #1

Homework Statement



Estimate the kinetic energy of a constituent quark of mass 300 MeV/c^2 confined insdide a proton of radius 1 fm

Homework Equations



Heisenberg's uncertainty principle [tex]\Delta x \Delta p \approx \hbar[/tex] (1)
Kinetic energy [tex] T=\frac{p^2}{2m}[/tex] (2)

The Attempt at a Solution



So we've got [tex]\Delta x[/tex]. So we can rearrange (1) to get [tex]\Delta p[/tex]

Then we need to use (2). Is it OK to just say [tex]\Delta T = \frac{\Delta p^{2}}{2m}[/tex]

Alternatively could we use the relation that delta T = dT/dp delta p but then we'd need to know p as well. And how would we then use this to get T?

This should be easy, but I never know when to use the second method using differentiation and when not to. Cheers.
 

Answers and Replies

  • #2

Homework Statement



Estimate the kinetic energy of a constituent quark of mass 300 MeV/c^2 confined insdide a proton of radius 1 fm

The Attempt at a Solution



So we've got [tex]\Delta x[/tex]. So we can rearrange (1) to get [tex]\Delta p[/tex]

Then we need to use (2). Is it OK to just say [tex]\Delta T = \frac{\Delta p^{2}}{2m}[/tex]
That is perfectly fine.
 

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