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So, I have these 2 potential barrier diagrams for particles coming from the left, and my exercise is too graph corresponding T(E)graphs in detail taking into consideration what new effects that can occur and at what energy levels they occur.

I really don't know how to think on this problem, other than that I think that the first one should be 0 until it reaches E=V2 (for the particles to have enough energy to transmitt) were it should with some kind graph-form increase and has T=1 as an asymptote (for both diagrams) since Transmission increases with energy.

Thanks for any help. It is appreciated

Potential barrier diagrams - particles from left meet potentials

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  • $\begingroup$ Read through your material on quantum tunneling again. Tunneling has a nonzero probability even if the energy is below the minimum energy classically required. This is what makes it different from classical scattering. $\endgroup$ Commented Nov 28, 2019 at 16:00
  • $\begingroup$ If I understod the tunneling effect correctly, there has to be an area behind the barrier with lower potential, so for the barier not to be infinitive such as with V2 $\endgroup$
    – Hiqi1010
    Commented Nov 28, 2019 at 19:01

2 Answers 2

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"Tunneling" usually refers to transmission through a barrier higher than the energy of the particles, so this is not really "tunneling".

Your thinking is correct, but the $T(E)$ has oscillations due to reflections back and forth in the well. See for example the graph for "Quantum well" on this page.

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The short version is that to solve this problem you find the Schrodinger equation for each region, impose suitable boundary conditions at each interface and specify some initial conditions, then solve the resulting equations. This sort of treatment can be found in many quantum mechanics textbooks and here.

You can also do calculations using transfer matrices, see Section 2 of this paper:

https://arxiv.org/abs/1205.1318

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