Can Resonant Transmission happen when U > E?

  • Context: Graduate 
  • Thread starter Thread starter PsychonautQQ
  • Start date Start date
  • Tags Tags
    Resonant Transmission
Click For Summary
SUMMARY

Resonant transmission occurs when the energy (E) of a particle beam exceeds the potential barrier (U), resulting in oscillations in transmission probability. In contrast, when U exceeds E, the phenomenon of tunneling occurs, and resonant transmission does not apply. The discussion highlights the importance of understanding the mathematical derivation of these concepts, which is typically covered in quantum mechanics textbooks. The equations for transmission probability and energy relationships are crucial for grasping these principles.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly potential barriers.
  • Familiarity with transmission probability equations in quantum mechanics.
  • Basic algebra skills for deriving equations related to resonant transmission.
  • Knowledge of wave functions and their behavior in quantum systems.
NEXT STEPS
  • Study the derivation of transmission probability equations in quantum mechanics.
  • Learn about the concept of tunneling in quantum mechanics and its implications.
  • Explore the mathematical foundations of resonant transmission and its applications.
  • Review Griffiths' "Introduction to Quantum Mechanics" for a comprehensive understanding of these topics.
USEFUL FOR

Students of quantum mechanics, physicists, and anyone interested in the behavior of particle beams in potential barriers will benefit from this discussion.

PsychonautQQ
Messages
781
Reaction score
10
My textbook had a section where a particle beam was going over a barrier where E > U and then right after that had a part about resonant transmission. It then went on to talk about Tunneling through a barrier when U > E. It didn't give a new resonant transmission equation and i assume the equation would be different...

So yeah, if a particle beam is tunneling through a barrier (U>E) there is no resonant transmission?

P.S. what math skills should i have before investing in griffiths quantum intro?
 
Physics news on Phys.org
What do you call resonant transmission?
 
You can see the equations for transmission probability versus energy, and a graph, here:

http://en.wikipedia.org/wiki/Rectangular_potential_barrier

It also shows an outline of the derivation of these equations. The missing steps are a lot of algebra, and are a standard exercise in many QM textbooks.

By "resonant transmission" PsychonautQQ probably means that the transmission probability oscillates with energy when E > U (E > V0 in the Wikipedia page). The maxima are "resonances" of the wave inside the barrier.
 

Similar threads

Undergrad I want to understand how the transmission coefficient is obtained
  • · Replies 3 ·
Replies
3
Views
1K
E<V Potential Step Confusion
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Superluminal Quantum tunneling without FTL messaging
  • · Replies 14 ·
Replies
14
Views
2K
Graduate Why Can Electrons Tunnel Through Barriers in Quantum Mechanics?
  • · Replies 4 ·
Replies
4
Views
6K
Graduate Quantum properties and Van Hove singularty
  • · Replies 5 ·
Replies
5
Views
514
Undergrad What happens when a particle observes itself during quantum tunneling?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Massless fermions Klein tunneling
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Image force in normal metal electrode tunneling
  • · Replies 1 ·
Replies
1
Views
2K
Admissions Could I please get critique on my SOP? (Experimental Biophysics)
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Heaviside Step Potential - Tunneling
  • · Replies 3 ·
Replies
3
Views
3K