Time Dependent Perturbation with changes in potential wells. Consider an infinite potential well, inside a particle of m

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Time Dependent Perturbation With Changes In Potential Wells Consider An Infinite Potential Well Inside A Particle Of M 1 (33.76 KiB) Viewed 58 times

Time Dependent Perturbation with changes in potential wells. Consider an infinite potential well, inside a particle of mass m starts in the ground state with V(x) = 0 in the bounds of L/2 < x < L/2 outside of that V(x) = ∞ What if, a rectangular bump rises in the middle of the well at a constant rate of r causing V(x, t) = rt within - d/2 < x <d/2 with d < L V(x, t) = 0 everywhere else inside the well. 1) Which transitions from the ground state with energy E1 = n²h²/2mL² cannot take place due to this perturbation - think in terms of parity 2) Use first order perturbation theory to explicitly calculate the probability of transition to the second excited state E3 = 9E1 as the barrier rises as a function of time. Helpful things you can use 41(x) = √2/Lcos(xX/L) -1/2 -d/2 d/2 43(x) = √2/Lcos(3πx/L) L/2