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Question 2 2.1 Consider an infinite well for which the bottom is not flat, as sketched here. If the slope is small, the potential V=s |x|/ a may be considered as a perturbation on the square- well potential over -a/2 ≤x≤a/2. V(x) -a/2 a/2 Calculate the ground-state energy, correct to first order in perturbation theory. Given (0) Ground state of box of size a: 40 = √² cos Ground state energy: E h²k² = = 2m 2ma² -

Question 2 2.1 Consider an infinite well for which the bottom is not flat, as sketched here. If the slope is small, the potential V=s |x|/ a may be considered as a perturbation on the square- well potential over -a/2 ≤x≤a/2. V(x) -a/2 a/2 Calculate the ground-state energy, correct to first order in perturbation theory. Given (0) Ground state of box of size a: 40 = √² cos Ground state energy: E h²k² = = 2m 2ma² -

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Question 2 2.1 Consider an infinite well for which the bottom is not flat, as sketched here. If the slope is small, the potential V = 6 |x|/ a may be considered as a perturbation on the square- well potential over -a/2 ≤x≤a/2. -8 W V(x) a/2 -a/2 X Calculate the ground-state energy, correct to first order in perturbation theory. Given (0) = √²/co COS Ground state of box of size a: = Ground state energy: E(0) = 4²k² 2ma². 0 Y
Transcribed Image Text:Question 2 2.1 Consider an infinite well for which the bottom is not flat, as sketched here. If the slope is small, the potential V = 6 |x|/ a may be considered as a perturbation on the square- well potential over -a/2 ≤x≤a/2. -8 W V(x) a/2 -a/2 X Calculate the ground-state energy, correct to first order in perturbation theory. Given (0) = √²/co COS Ground state of box of size a: = Ground state energy: E(0) = 4²k² 2ma². 0 Y
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