Transmission probability (tunneling) question

Click For Summary
SUMMARY

The discussion centers on calculating the width of a potential barrier that maximizes reflection for a beam of 11 eV electrons encountering a barrier of potential Vo = 3.8 eV. The transmission probability formula provided is T = [ 1 + (Vo²*sin²(βa))/(4E*(E - Vo)) ]^(-1), where 'a' represents the barrier width. The user expresses confusion regarding the concept of maximum reflection not equating to 100% reflection and seeks guidance on how to approach the problem, particularly in relation to derivatives and the reflection coefficient.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly tunneling phenomena.
  • Familiarity with the concept of potential barriers and energy levels in quantum systems.
  • Knowledge of the mathematical derivation of transmission and reflection coefficients.
  • Basic calculus, specifically the application of derivatives to find maxima.
NEXT STEPS
  • Study the derivation of the transmission probability formula for quantum tunneling.
  • Learn about the relationship between barrier width and reflection coefficients in quantum mechanics.
  • Explore the concept of β in quantum tunneling and its calculation.
  • Investigate the implications of non-100% reflection in quantum systems and its physical significance.
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics, as well as researchers interested in tunneling phenomena and barrier interactions.

mclame22
Messages
10
Reaction score
0
A beam of 11 eV electrons is directed towards a barrier of potential Vo = 3.8 eV. Compute the width of the barrier for which the reflection is maximized (Note: this is NOT asking for when reflection is 100%).

Transmission probability for E > Vo:
T = [ 1 + (Vo²*sin²(βa))/(4E*(E - Vo)) ]^(-1)

where a is the width of the barrier.

I need a bit of help starting this question. I do not understand why maximum reflection is not 100% reflection, or T = 0. Finding when something is a maximum makes me think "derivative = 0," but other than that I'm really unsure about where to go. And there is a formula for β but I am not very concerned with numerical answers right now. Any advice is appreciated.
 
Physics news on Phys.org
Why would you expect the reflection coefficient to be 1?
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
Replies
2
Views
5K
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
Replies
9
Views
3K
  • · Replies 5 ·
Replies
5
Views
11K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K