Quantum Tunneling Across a Square Barrier

In summary, the problem involves estimating the transmission coefficient for 7 eV electrons penetrating a 10 eV barrier created by an insulating oxide layer with thicknesses of 5 nm and 1 nm. The solution involves understanding and applying equations related to tunneling. After receiving a hint, the person was able to solve the problem by using the correct values in the equation.
  • #1
div4200
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Homework Statement



Two copper conducting wires are separated by an insulating oxide layer. This layer acts as a square
barrier of height 10 eV. Estimate the transmission coefficient for penetration by 7 eV electrons (a) if the
layer thickness if 5 nm and (b) if the layer thickness is 1 nm

Homework Equations



I don't know. That is the problem.

The Attempt at a Solution



I don't even know where to start. I'm not asking for someone to do the problem for me. I just want a hint in the right direction. Thanks a lot!
 
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  • #2
Well, for starters, what do you know (or can look up) about tunneling? Do you know what it is? Do you know any equations that apply to it?
 
  • #3
I just figured it out actually. My problem was that I was using an equation in my textbook with the wrong values. Thanks!
 

1. What is quantum tunneling across a square barrier?

Quantum tunneling refers to the phenomenon in which a particle can pass through a potential energy barrier even though it does not have enough energy to overcome the barrier. In the case of a square barrier, the potential energy is constant within a certain region and then abruptly drops to zero, creating a barrier that the particle must tunnel through.

2. Why is quantum tunneling across a square barrier important?

Quantum tunneling is a fundamental concept in quantum mechanics and plays a crucial role in many physical phenomena. It is essential in understanding the behavior of particles at the atomic and subatomic level, and it has practical applications in fields such as electronics, nuclear physics, and chemistry.

3. What factors affect the probability of quantum tunneling across a square barrier?

The probability of quantum tunneling is influenced by several factors, including the height and width of the barrier, the mass and energy of the particle, and the shape of the potential energy curve. Furthermore, the temperature and the presence of other particles can also affect the probability of tunneling.

4. Can quantum tunneling occur for macroscopic objects?

No, quantum tunneling is a phenomenon that only occurs at the quantum level. While it may seem counterintuitive, classical objects that we encounter in our daily lives do not exhibit quantum tunneling. This is because the wavelength of macroscopic objects is much smaller than the size of the barrier they would need to tunnel through, making the probability of tunneling virtually zero.

5. How is quantum tunneling across a square barrier related to the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. In the case of quantum tunneling, the particle is within the barrier despite not having enough energy to overcome it. This violates the principle, but it is allowed due to the probabilistic nature of quantum mechanics.

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