Question: 4) Consider a system in a simple harmonic oscillator potential V (x) =mw?x?. At time t= 0, a particle is in the state Y(x,0) =

4) Consider a system in a simple harmonic oscillator potential V

4) Consider a system in a simple harmonic oscillator potential V (x) =mw?x?. At time t= 0, a particle is in the state Y(x,0) = A ( V. - V3 -22). a) Normalize the wavefunction. Show your work. b) Find (x,t) and I '(x,t)1. Do they oscillate with time? If so, what is the frequency? Show your work. c) Calculate . Does it change with time? Show your work. d) What is the probability that a measurement of energy would yield E = 5/2 w at time t=0? Show your work and explain. 4) Consider a system in a simple harmonic oscillator potential V (x) =mw?x?. At time t= 0, a particle is in the state Y(x,0) = A ( V. - V3 -22). a) Normalize the wavefunction. Show your work. b) Find (x,t) and I '(x,t)1. Do they oscillate with time? If so, what is the frequency? Show your work. c) Calculate . Does it change with time? Show your work. d) What is the probability that a measurement of energy would yield E = 5/2 w at time t=0? Show your work and explain

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