(a) [10 marks] A particle of mass m and charge q moves in a one-dimensional infinite square-well potential 0, |x|

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A 10 Marks A Particle Of Mass M And Charge Q Moves In A One Dimensional Infinite Square Well Potential 0 X L V X 1 (76.09 KiB) Viewed 22 times

(a) [10 marks] A particle of mass m and charge q moves in a one-dimensional infinite square-well potential 0, |x|<L V(x) = ∞, x > L of width 2L. A weak, constant in time, electric field & is applied to the particle with a resulting perturbation Ĥ' = -qεâ. Find the first non-vanishing correction to the ground state energy. (b) [10 marks] Consider now the case where the electric field has time-dependence given by Eoe-t/T, t>0 E= t < 0 where and are constants. Calculate, to leading order in & and when t > T, the probability for the system to transition from the ground state to the first excited state. 11 01