Please do all three parts. Show all procedures please. Thank you! Assume A(k) =
ID: 1526561 • Letter: P
Question
Please do all three parts.
Show all procedures please.
Thank you!
Assume A(k) = A_o e^-(k - k_o)^2/2 sigma^2 - a Gaussian spread function for the particle in 'k' space, where omega = E/h = hk^2/2m* is for a free particle with 'effective' mass m*. (a) Find the mean value of the wave vector k and its uncertainty defined as delta k = [Delta k^2]^1/2, where Delta k = k - k. You should be able to show Delta x^2 = x^2 -(x)^2 (b) Find the mean value of the location (centroid) of the particle x and its uncertainty defined as delta x = delta x = [Delta x^2]^1/2, where Delta x = x - x. (c) Find the product delta x delta x as a function of time 't'. Starting at t = 0, interpret your result in terms of the Heisenberg Uncertainty Principle.Explanation / Answer
1) wave vector k=(2pi/wavelength)
we know effective mass(m*) =[ h(croos)2 /d2 E/dK2 ]
[m* =h(cross)2 k2 /2E] from given relation
from these two we get
[k2 /2E]=[dk2 /dE2 ]
heisenberg uncertinity principle states that the product of uncertainity in position and momentum of a particle is always greater then or equal to h(cross).
it means if we know the position , the momentum is less likely to determine and vice versa.