ch39-p019 - 19. Schrdingers equation for the region x >...

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19. Schrödinger’s equation for the region x > L is d dx m h EU 2 2 2 2 0 8 0 ψ +− = π . If = De 2 kx , then d 2 / dx 2 = 4 k 2 De 2 kx = 4 k 2 and d dx m h k m h 2 2 2 2 0 2 2 2 0 8 4 8 ψψ = ππ This is zero provided k h mU E =− π 2 0 bg The proposed function satisfies Schrödinger’s equation provided k has this value. Since U 0 is greater than E in the region x > L , the quantity under the radical is positive. This means k is real. If k is positive, however, the proposed function is physically unrealistic.
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