Please explain in step-wise and legible manner.

Chem 5 Problem 2 [20pts] In quantum mechanics the state of a system is often expressed by in the position representation of the wavefunction y(x) with a probability distribution calculated according to its square modulus, (1*1) = ly/2. However we can equivalently compute quantities in the momentum representation of the wavefunction, (p). The position and momentum representations of the wavefunction are an instance of a Fourier Pair and related accordingly, 1(x) = V2 Tch Lap + (ple'pxin $(p) = VETTh / o dx up ( x)e -ipxin Using this information calculate the momentum representation, do(p), of the ground state for the quantum harmonic oscillator whose position representation wavefunction is yo(x) = ( mw ) 1/4 mx-w Tch exp 2h for a particle of mass m and oscillating with frequency w. Report you answer simplified and in terms of m, w, and h. Hint. Recall, dre ( ax +6x ) = It 62 / 4a Draw a box around your final equation for po(p). Show your work for each step explicitly