I don't understand how a particle can exist with negative kinetic energy. Consider this scenario: Electron tunneling through Potential barrier

Here, an electron is tunneling through a potential barrier (The total energy of the electron is less than the potential barrier).

So the math works out pretty well and we find that the wave function has a finite value on the left of the barrier, inside the barrier and also to the right of the barrier.

I'm unable to grasp what is actually happening inside the barrier though:
Like if I make a measurement and the particle turns out to be inside the barrier (it can since the wave function is finite over there), then will we find it there with negative kinetic energy (since potential is greater than total energy)?

Could you explain what actually happens? Do we find it with negative KE and if so, then what does this even imply physically?
Or does the particle get extra energy from somewhere and we find it with non-negative KE and if so, where does it get the energy from?

  • $\begingroup$ I am not 100% sure of the physical interpretation, there's smarter people than me to answer that, but do remember that a particle localized at a small region, whether inside or outside the barrier, doesn't really have a specific kinetic energy, as per the Uncertainty Principle. $\endgroup$ – Phineas Nicolson Nov 6 '20 at 14:10
  • $\begingroup$ But once we measure it, its wave function will collapse. And now it should have some specific kinetic energy right? @PhineasNicolson $\endgroup$ – Shreyas Pradhan Nov 7 '20 at 15:39
  • $\begingroup$ No, specific kinetic energy requires specific momentum and since, after measurement, the particle has a very specific position, it can't have a specific momentum. If, on the other hand, you were to measure the momentum of the particle, and thus its kinetic energy very precisely, the particle's state would collapse to one with a specific momentum, so it can't have a specific position. $\endgroup$ – Phineas Nicolson Nov 8 '20 at 2:45
  • $\begingroup$ So if you measure a specific kinetic energy for the particle, you can no longer refer to it as being inside or outside the barrier. $\endgroup$ – Phineas Nicolson Nov 8 '20 at 2:46

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