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EE 400B Homework #4 Solution
1. (20%) Griffiths, Problem 2.35 (a) and (c). (Solution for (b) is also included.)
2. (30%) (a) Calculate the transmission coefficient for an electron of total energy 2 eV incident
upon a rectangular potential barrier of height 4 eV and thickness 0.1 nm. (b) If a particle
twice the mass of an electron with the same energy tries to penetrate this barrier, what would
be the probability of transmission? Please predict, qualitatively, if it would be higher or lower
than the transmission coefficient for an electron, then verify your prediction by calculation.
(c) If the electron energy is allowed to increase to above the potential barrier, at what lowest
energy will the transmission coefficient become 1?
(a) kII a 
2mV0 a 2  E 
2  9.11031  4 1.6 1019 1020  2 
1




1    0.727
2
(1.05 1034 ) 2
 4
 V0 
1




sinh 2 k II a 

T  1
 0.716

E
E 
 4 1   
V0  V0  

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(b) With higher mass but the same kinetic energy, the particle would have lower speed and
therefore would be attenuated faster  lower transmission probability.
If the mass becomes 2m, kII a  2  0.727  1.028
 T  0.621
(c) T = 1 when kIII a  
2mV0 a 2  E 
2  9.11031  4 1.6 1019 1020  E 
kIII a 
  1 
  1  
2
(1.05 1034 )2
 V0 
 V0 
 E  10.3V0  40.6 eV
3. (30%) Griffiths, Problem 2.47.
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4. (20%) Griffiths, Problem 5.5.
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