p40_022 - k is real and the proposed function satisFes Schr...

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22. (a) and (b) In the region 0 <x<L , U 0 =0,soSchr¨ odinger’s equation for the region is d 2 ψ dx 2 + 8 π 2 m h 2 =0 where E> 0. If ψ 2 ( x )= B sin 2 kx ,then ψ ( x )= B 0 sin kx ,where B 0 is another constant satisfying B 0 2 = B .Thu s d 2 ψ/dx 2 = k 2 B 0 sin kx = k 2 ψ ( x )and d 2 ψ dx 2 + 8 π 2 m h 2 = k 2 ψ + 8 π 2 m h 2 Eψ . This is zero provided that k 2 = 8 π 2 mE h 2 .
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Unformatted text preview: k is real and the proposed function satisFes Schr odingers equation. In this case, there exists no physical restriction as to the sign of k . It can assume either positive or negative values. Thus k = 2 h 2 mE ....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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