Transmission of a TWO step potential

In summary, to evaluate the transmission coefficient for the incident wave into the region x>a, you will need to consider the potential function V(x) with 2 steps, at x=0 and x=a. This will result in 2 boundary conditions that will affect the answer. After solving for the wavefunction with these boundary conditions, you can then use your usual method to calculate the transmission coefficient.
  • #1
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Homework Statement


Consider the potential:
V(x)
=0 x<0
=V1 0<x<a
=V2 x>a

Where 0<V1<V2 and E>V2

Evaluate the transmission coefficient for the incident wave into the region x>a


Homework Equations


T= 4k0k1/((k0+k1)^2)


The Attempt at a Solution


I have not attempted this. It seems pretty straight forward if there were only ONE step. How does the fact that there are two steps factor into the answer?

Thank you.
 
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  • #2
You will have 2 boundary conditions which can affect your answer. Since a wave traveling from the far left will interact with both of them, and some of it will reflect back at both steps.

Just solve for the wavefunction with the 2 BC's, and solve for the transmission the way you usually do after that.
 

1. What is a TWO step potential?

A TWO step potential refers to a type of potential energy function that has two distinct regions with different energy levels. It can be represented as a step-like shape on a graph, hence the name.

2. How is the transmission of a TWO step potential calculated?

The transmission of a TWO step potential is calculated using the Schrödinger equation, which takes into account the potential energy function and the wave function of the particle. The transmission coefficient is then obtained by solving the Schrödinger equation for both regions of the potential and comparing the wave amplitudes on either side.

3. What factors affect the transmission of a TWO step potential?

The transmission of a TWO step potential is affected by various factors such as the height and width of the potential barriers, the energy of the particle, and the angle of incidence. The transmission coefficient also depends on the mass and wavelength of the particle.

4. Can the transmission of a TWO step potential be controlled?

Yes, the transmission of a TWO step potential can be controlled by adjusting the parameters of the potential energy function. This can be done by changing the shape, height, or width of the potential barriers. Additionally, the transmission can also be influenced by the energy and properties of the particle.

5. What is the significance of studying the transmission of a TWO step potential?

Studying the transmission of a TWO step potential is important in understanding the behavior of particles in different potential energy landscapes. It has applications in fields such as quantum mechanics, solid state physics, and nanotechnology. It also provides insights into the behavior of particles in barrier structures, which is crucial in the development of various technologies and devices.

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