At time t = 0 a particle at a potential V (x) = mwX?/2 is in...

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At time t = 0 a particle at a potential V (x) = mwX?/2 is in the state described by the wave function v (r,0) = AE) vn(a), n=0 Where n (x) are the normalized eigenstates with their respective energies En = hw(n + 1/2). %3D (a) Find the normalization constant А. (b) Find the expression of (x, t) for t> 0. (c) Show that |(x, t)² is a periodic function of time, and indicate which is the period t (d) Find the mean value of the energy (E)att = 0. (e) Determine the mean value (E) (t) of the energy as a function of time 6. At time t = 0 a particle at a potential V (x) = mwX?/2 is in the state described by the wave function v (r,0) = AE) vn(a), n=0 Where n (x) are the normalized eigenstates with their respective energies En = hw(n + 1/2). %3D (a) Find the normalization constant А. (b) Find the expression of (x, t) for t> 0. (c) Show that |(x, t)² is a periodic function of time, and indicate which is the period t (d) Find the mean value of the energy (E)att = 0. (e) Determine the mean value (E) (t) of the energy as a function of time 6.