Given a time-dependent one-dimensional quantum harmonic oscillator defined by the Hamiltonian
;
with q0(t) = t/T and t ∈ [0 : T]. Given |ψ0i = |n = 0i (ground state of the Harmonic oscillator), compute |ψ(t)i for different values of T. Plot the square norm of |ψ(t)i as a function of q at different times, and the average position of the particle as a function of t.
