What Is the Tunnel Effect in Time-Independent Quantum Mechanics?

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Discussion Overview

The discussion centers around the tunnel effect in time-independent quantum mechanics, specifically examining the conditions under which particles can tunnel through a potential barrier. Participants explore the implications of the time-independent Schrödinger equation and the conservation of energy in this context.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant describes a potential barrier scenario using the time-independent Schrödinger equation, questioning how tunneling can be discussed when energy is conserved and particles have the same energy before and after the barrier.
  • Another participant asserts that conservation of energy should imply no change in energy during tunneling.
  • A different participant raises a concern about the absence of energy dissipation when particles interact with the potential barrier, linking this to the uncertainty principle.
  • Another reply suggests that if there were energy dissipation, the evolution of the wavefunction would not be reversible, indicating a significant deviation from typical quantum behavior.

Areas of Agreement / Disagreement

Participants express differing views on the implications of energy conservation and the nature of tunneling in time-independent scenarios. The discussion remains unresolved regarding the role of energy dissipation and its effects on tunneling.

Contextual Notes

Participants do not fully explore the implications of the uncertainty principle in relation to the tunneling effect, nor do they clarify the assumptions underlying their arguments about energy dissipation and wavefunction behavior.

LagrangeEuler
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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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Conservation of energy. Why do you think it would be different?
 
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}##.
 
The evolution of the wavefunction would not be reversible (or very highly unlikely to be reversible) if there were dissipation.
 

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