Consider a harmonic oscillator with mass m and angular frequency omega. Its 6 th energy eigenstate is known to be psi_(6)(x)=(1)/(C_(6))H_(6)((x)/(a))e^(-(x^(2))/(2a^(2))), where H_(6)(X)=64X^(6)-480X^(4)+720X^(2)-120 is the 6 th Hermite polynomial, a-=sqrt((h)/(m omega)) is the typical length scale of the harmonic oscillator, and C_(6)=sqrt(2^(6)6!asqrtpi) is the normalization factor. (a) Determine the Fourier transform of the wavefunction tilde(psi)_(6)(k)-=(1)/(sqrt(2pi))intpsi_(6)(x)e^(-ikx)dx up to a phase factor: (8 marks) (b) At t=0, the harmonic oscillator is initially prepared in the state (not an eigenstate) psi(x,0)=(1)/(A)e^(-((x-x_(0))^(2))/(2b^(2))), where b and x_(0) are constants and A is the normalization factor. Find the expectation values