The top is little bit of background about the subject. If you decide to solve it on paper please use clear handwriting. Thank you

Sub Problem 2: Looking at the packet in k-space We talked about a particle in a box and how any wavefunction can be written in terms of the particle-in-a box stationary states. Similarly, any good wavefunction for a free particle can be expressed in terms of plane waves, as they are the stationary solutions for the free particle problem: ELt ikx OO OO Note that c(k) is simply a Fourier amplitude of PX,0) Just like ly(x. 0) I told about the distribution of position, Ic k) is the probability density of a particle having a certain wave vector k. a) Calculate c (k) nt: you will obtain a Gaussian) b) Plot Ic(k) as a function of k (k should be in terms of the natural k-units of the problem, i.e. 1/ G) c) Just by looking at the shape of c(k) and inspecting its formula obtained under a), what would you say (k) and Ak should be? (Hint: since the wavepacket is a Gaussian in both x and k, if some characteristic features of the Gaussian in real space relate to (x) and Ax, then analogous features of the Gaussian in k-space relate to (k) and Ak d) How does Ak obtained above from the shape of I c(k compare to the uncertainty of wave number you would get from Problem le? Use Ap hAk