p40_023 - 23. Schrdingers equation for the region x > L...

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23. Schr¨ odinger’s equation for the region x>L is d 2 ψ dx 2 + 8 π 2 m h 2 [ E U 0 ] ψ =0 . If ψ = De 2 kx ,then d 2 ψ/dx 2 =4 k 2 De 2 kx =4 k 2 ψ and d 2 ψ dx 2 + 8 π 2 m h 2 [ E U 0 ] ψ =4 k 2 ψ + 8 π 2 m h 2 [ E U 0 ] ψ. This is zero provided k = π h p 2 m ( U 0 E ) . The proposed function satisFes Schr¨ odinger’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
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