Tunnel Effect in Quantum Mechanics: Exploring Time-Independent Problems

In summary, the conversation discusses the phenomenon of tunneling in quantum mechanics, specifically in the case of a time-independent Schrodinger equation with a potential barrier. It is noted that the energy of the particles before and after the barrier remains the same, due to conservation of energy. The potential for dissipation of energy is brought up, but it is explained that the lack of reversibility in the wavefunction evolution suggests that there is no dissipation in this scenario.
  • #1
LagrangeEuler
717
20
In case of tunnel effect in quantum mechanics we often consider time independent Schroedinger equation with potential ##0##, when ##x<0## then some ##V_0## when ##0\leq x\leq a## and ##0## when ##x>a## so potential barrier problem. And energy of particle that we send to barrier is ##E<V_0##. In that case energy of the particles that past barrier will be the same as energy of particles before barrier. Why is that case? How we could even talk about tunneling in case of time independent problem?
 
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  • #2
Conservation of energy. Why do you think it would be different?
 
  • #3
Yes I know that is conservation of energy. But why there do not exists some dissipation of energy when particles interact with potential ##V_0##. When we have time dependent solution we have also uncertainty
relation ##\Delta E \Delta t \approx\frac{\hbar}{2}##.
 
  • #4
The evolution of the wavefunction would not be reversible (or very highly unlikely to be reversible) if there were dissipation.
 

1. What is the tunnel effect in quantum mechanics?

The tunnel effect, also known as quantum tunneling, is a phenomenon in quantum mechanics where a particle has a non-zero probability of crossing through a potential barrier, even though it does not have enough energy to do so based on classical physics.

2. How does the tunnel effect work?

The tunnel effect occurs due to the wave-like nature of particles in quantum mechanics. According to the uncertainty principle, there is always a small probability that a particle can exist in a region where its energy is lower than the potential barrier. This allows the particle to "tunnel" through the barrier and appear on the other side.

3. What are some real-world applications of the tunnel effect?

The tunnel effect is an important concept in the development of electronic devices, such as transistors and flash memory. It also plays a role in nuclear fusion reactions and radioactive decay. Additionally, the tunnel effect is used in scanning tunneling microscopy, which allows scientists to see and manipulate individual atoms on a surface.

4. Can the tunnel effect be observed in everyday life?

While the tunnel effect is constantly occurring in the microscopic world, it is not typically observed in everyday life due to the extremely small scales involved. However, some macroscopic systems, such as superconductors and superfluids, exhibit quantum tunneling behavior that can be observed under certain conditions.

5. What are some time-independent problems in relation to the tunnel effect?

Time-independent problems in quantum mechanics refer to situations where the potential barrier does not change over time. This allows for the use of stationary state solutions to solve the Schrödinger equation, making the calculation of tunneling probabilities more straightforward. Examples of time-independent problems include particle scattering and tunneling through potential barriers.

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