6: A particle in a harmonic oscillator potential (V(:L*) = %km2) has a normalized proba bility distribution described by 114$) : ice\"2:62. Obtain the Fourier Transform of this J} 1 0 . positiondependent distribution using: 9(a) = F / 'Il(m)e_m$dm. 9(a) is essentially 7T oo the normalized momentum distribution for the particle. Hints: You will need to complete the square in the exponential function. Then you need to change variables and eventually use the trick for integrating a Gaussian (that we saw earlier in the semester when we discussed the Gaussian probability distribution). If you are interested, the a2 = \\/ [cm/h where k is the effective spring constant, m is the particle mass and h is Planck's constant divided by 271