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can anyone please help me with this question? I know it is tedious and hard but...

can anyone please help me with this question? I know it is tedious and hard but if you can help me with full step by step solutions, I will really be grateful. I'm also sorry that this question has multiple parts.

Question 3: Consider a charged particle in a harmonic oscillator potential in one dimension with an electric field turned on at t0 2m 2 10 2m 2 (a) Calculate the correction to the energy levels due to the electric field to the lowest non-vanishing order in perturbation theory (b) What are the exact energy levels for the system at t > 0? (c) Assuming the particle to be in the ground state of Ho at t-0, find the probability of finding it in the 1st excited state of Ho at a later time tj after the field has been turned on. What is the probability of finding it in the 2nd excited state? (6 pt) (4 pt) (4 pt)

Question 3: Consider a charged particle in a harmonic oscillator potential in one dimension with an electric field turned on at t0 2m 2 10 2m 2 (a) Calculate the correction to the energy levels due to the electric field to the lowest non-vanishing order in perturbation theory (b) What are the exact energy levels for the system at t > 0? (c) Assuming the particle to be in the ground state of Ho at t-0, find the probability of finding it in the 1st excited state of Ho at a later time tj after the field has been turned on. What is the probability of finding it in the 2nd excited state? (6 pt) (4 pt) (4 pt)
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