Where does the energy come from?

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SUMMARY

The discussion centers on the quantum tunneling phenomenon where electrons can pass through a potential barrier even when the barrier's potential energy (V) exceeds the energy provided by an electrostatic accelerator (U). Participants clarify that this does not violate the conservation of energy, as energy conservation in quantum mechanics is upheld through the Hamiltonian formalism. The conversation explores the implications of wave functions, measurement processes, and the probabilistic nature of quantum mechanics, emphasizing that particles can exist in regions of higher potential without requiring additional energy from external sources.

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  • Understanding of quantum mechanics principles, particularly the tunneling effect.
  • Familiarity with the Hamiltonian formalism in quantum theory.
  • Knowledge of wave functions and their probabilistic interpretations.
  • Concept of energy eigenstates and their implications in measurements.
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  • Study the quantum tunneling phenomenon in detail, focusing on its applications in semiconductor physics.
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  • #31
Thus we wouldn't even have to ask the question that started this thread ("where does the energy come from?") if we interpret the wave function as giving the probability that the electron will be detected in the classically forbidden zone, rather than as the probability that the electron is violating conservation of energy by being there.
Why do you think so - do you think that when the electron is detected, the description of such process including the detector will be such that the total energy is conserved?
 
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  • #32
If you include the detector in the description then the total energy is conserved.

For example, if you have an electron gun at 0V firing 10keV electrons at a -11kV wall, then they're supposed to be reflected. Now if you put a probe in the forbidden region near the wall, you should be able to get some current in the probe. The probe is at some voltage > -10kV, so the electrons are allowed to propagate in the probe. You can measure the energy of the electrons in the probe by looking at the IV characteristics.

You can't directly measure a negative energy electron, but once the electron appears on the other side of the barrier (and has positive k. energy again), you can check that the energy was indeed conserved.
 

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