Where does the energy come from?

  • Context: Graduate 
  • Thread starter Thread starter Jano L.
  • Start date Start date
  • Tags Tags
    Energy
Click For Summary

Discussion Overview

The discussion revolves around the implications of quantum tunneling in a macroscopic setup involving an electrostatic accelerator and a potential barrier. Participants explore the conservation of energy in scenarios where electrons appear to penetrate regions of higher potential energy than their initial state, raising questions about the nature of energy transfer and measurement in quantum mechanics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that electrons can arrive at a detector even when the potential barrier is higher than the accelerating potential due to the tunneling effect, questioning if this contradicts conservation of energy.
  • Others argue that energy conservation must hold in quantum mechanics, suggesting that additional energy must be provided for electrons to reach the detector in a higher potential region.
  • There is a discussion about the nature of wave packets and energy eigenstates, with some participants noting that a wave packet does not have a definite energy, complicating the application of energy conservation.
  • Participants raise concerns about the measurement process and its implications for energy states, suggesting that measuring an electron in a forbidden region leads to a violation of energy conservation.
  • Some participants propose that the energy of the measurement apparatus must be considered, as it may be entangled with the energy of the electron state.
  • Questions are raised about the interpretation of probabilities in tunneling, with one participant challenging the assumption that a certain percentage of electrons tunneling implies a corresponding probability of the barrier stopping them.

Areas of Agreement / Disagreement

Participants express differing views on the implications of quantum tunneling for energy conservation, with no consensus reached on how energy is accounted for in these scenarios. The discussion remains unresolved regarding the relationship between tunneling, measurement, and energy conservation.

Contextual Notes

Participants highlight limitations in the understanding of energy conservation in quantum mechanics, particularly in relation to measurement processes and the nature of wave functions. There is also mention of unresolved mathematical steps and assumptions regarding the behavior of particles in potential barriers.

  • #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?
 
Physics news on Phys.org
  • #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.
 

Similar threads

Undergrad Where does the energy come from?
  • · Replies 21 ·
Replies
21
Views
2K
Undergrad What is the true nature of microscopic particles when not interacting?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad The Potential of Back-to-Back Photons: an Experiment
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Potential Energy of an Electron-Nuclei Interaction in DFT
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Source of energy for quantum tunneling of a particle
  • · Replies 27 ·
Replies
27
Views
3K
Graduate What is the quantum picture of laser field accelerating free electrons?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Photoelectric effect and Saturation Current
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Avalanche photon detectors
  • · Replies 0 ·
Replies
0
Views
546
Undergrad Energy of an electron with Schrodinger's equation
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Why Can Electrons Tunnel Through Barriers in Quantum Mechanics?
  • · Replies 4 ·
Replies
4
Views
6K