Answers to Sample Hour Exam #2

Answers to Sample Hour Exam #2 - h 1 1 1 2 2 ik x mE x H e...

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Answers to Sample Hour Exam #2 (It is suggested that you try to work the problems yourself before consulting the following)) MULTIPLE CHOICE 1. B 2. D 3. B 4. D 5. A 6. C TRUE/FALSE 1. T 2. T 3. F 4. F 5. T 6. T PROBLEMS 1. a) ( x , y , z )= x ( x ) y ( y) z ( z) x ( x )= A sin k x x ; k x = n x / L ; n x = 1, 2, 3, … (note n x >0 only). g( k ) = 2 V / 3
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b) g ’( k ) = V k 2 / 2 c) 3 2 1 2 2 2 2 2 V m Z E E h 2. a) None b) E > 0 c) Regions 2, 4 have evanescent waves; Regions 1, 3 have oscillating waves d) Since the electron is incident from the right, it must have E > U 1 . 4 4 1 4 4 2 2 ; ik x ik x m E U x Ae Be k h (the A term is the incident wave; the B term is the reflected wave). 3 3 3 3 2 2 ; ik x ik x o m E U x C e De k h 2 2 1 2 2 4 2 2 ; ik x ik x m E U x F e G e
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Unformatted text preview: h 1 1 1 2 2 ; ik x mE x H e k h (the H term is the transmitted wave). e) 2 3 a a implies 3 3 2 2 ik a ik a ik a ik a C e De F e Ge 2 3 a a implies 3 3 2 2 3 3 2 2 ik a ik a ik a ik a ik C e ik De ik F e ik Ge or (simplifying) 3 3 2 2 3 3 2 2 ik a ik a ik a ik a k C e k De k F e k Ge . f) 2 4 1 1 since and t i t i J H E k k T J J J A E U m m h h...
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