(adsbygoogle = window.adsbygoogle || []).push({}); 1.

this is for a particle in a box (infinite potential well):

For the wave functions calculate (as a function of n)

[tex]\Delta[/tex]x

[tex]\Delta[/tex]p

[tex]\Delta[/tex]x[tex]\Delta[/tex]p

2. Relevant equations

h = h bar below

u^{+}_{n}(x)=(1/[tex]\sqrt{a}[/tex] )cos((n-1/2)(pi)x/a)

u^{-}_{n}(x)=(1/sqrt{a})sin(n(pi)x/a)

E^{-}_{n}=h^{2}/(2m)(n(pi)/a)^{2}

E^{+}_{n}=h^{2}/(2m)((n-1/2)(pi)/a)^{2}

3. The attempt at a solution

ok i think the Delta x is easy, just find the variance of u^{+}_{n}(x)^{2}and u^{-}_{n}(x)^{2}as a function of n (correct me if i am wrong)

where i am lost is on the momentum, i can obviously get it from the energy but i don't see how to determine its variance or even how it would change within one state. i would just use the uncertainty principle but that seems to be what they want you to show in the next step (also it is an inequality not an exact equation)

thanks for any help and sorry if this is an absurd question, it has been awhile since i have done any of this sort of stuff.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Particle in a box momentum uncertainty

**Physics Forums | Science Articles, Homework Help, Discussion**