Can Resonant Transmission happen when U > E?

In summary, the conversation discussed the concept of resonant transmission in the context of a particle beam passing through a barrier with different energy levels. It was noted that the textbook did not provide a specific equation for resonant transmission in cases where the energy of the particle beam is greater than the potential barrier. The conversation also mentioned the necessary math skills for studying quantum mechanics and provided a link to a resource for further understanding of the equations and derivation of them. The term "resonant transmission" was clarified as being related to the oscillating transmission probability at certain energy levels.
  • #1
PsychonautQQ
784
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?
 
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  • #2
What do you call resonant transmission?
 
  • #3
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.
 

FAQ: Can Resonant Transmission happen when U > E?

1. Can resonant transmission occur when the energy of the particle is greater than the potential energy barrier?

Yes, resonant transmission can occur when the energy of the particle is greater than the potential energy barrier. This is known as over-the-barrier transmission and can happen if the barrier is not high enough or if the particle has enough energy to overcome the barrier.

2. How does resonant transmission differ from normal transmission?

Resonant transmission occurs when a particle's energy matches the energy of a bound state in the potential barrier, allowing the particle to tunnel through with a significantly higher probability. In contrast, normal transmission refers to when a particle has enough energy to overcome the barrier without matching a bound state.

3. What factors affect the likelihood of resonant transmission occurring?

The energy of the particle, the height and width of the potential barrier, and the presence of bound states in the barrier all affect the likelihood of resonant transmission occurring. Additionally, the symmetry of the potential barrier and the angle of incidence of the particle can also play a role.

4. Can multiple resonant transmission peaks occur for a single particle?

Yes, it is possible for multiple resonant transmission peaks to occur for a single particle. This can happen if there are multiple bound states in the potential barrier that the particle can match with its energy.

5. How is resonant transmission relevant in real-world applications?

Resonant transmission is relevant in many fields of physics, including quantum mechanics and solid-state physics. It is also important in technology, such as in the design of electronic devices and in the development of quantum computing. Additionally, resonant transmission has implications in fields such as nuclear physics and astrophysics.

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