Heisenberg Uncertainty Derivation

[XJellieBX]

Homework Statement

Using the uncertainty relation for momentum and position, show that the quantum-mechanical uncertainty in the position of a particle at temperture T is
\Delta x~\sqrt{\frac{h^{2}}{4mkT}}
where T is the temperature and k is the Boltzmann's constant.

Homework Equations

\Delta p\Delta x\geq h/2, h being Planck's constant
K.E.=0.5 mv²=0.5 kT

The Attempt at a Solution

I isolated \Delta x and subbed \Delta p=mv=kT/v.
So, \Delta x~h/2\Delta p ~ h/2mv ~ hv/2kT.
I've tried subing in a whole bunch of stuff for v but I can't seem to get the equation. Any insight?

 

[rl.bhat]

Homework Statement

Using the uncertainty relation for momentum and position, show that the quantum-mechanical uncertainty in the position of a particle at temperture T is
\Delta x~\sqrt{\frac{h^{2}}{4mkT}}
where T is the temperature and k is the Boltzmann's constant.

Homework Equations

\Delta p\Delta x\geq h/2, h being Planck's constant
K.E.=0.5 mv²=0.5 kT

The Attempt at a Solution

I isolated \Delta x and subbed \Delta p=mv=kT/v.
So, \Delta x~h/2\Delta p ~ h/2mv ~ hv/2kT.
I've tried subing in a whole bunch of stuff for v but I can't seem to get the equation. Any insight?

Delta p[/tex] = sqrt(2mE) where E is the kinetic energy which is equal to 1/2*kT

 

[XJellieBX]

Thanks =)