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In the Feynman lectures on Physics, he talks about quantum tunneling and, basically, there's a non-zero amplitude to be found in the barrier, where the particle's energy is below the rest mass, i.e. kinetic energy is negative, and because $E_k = p^2 / (2m)$, that implies $p$ is imaginary. Can this actually be observed? Can you collapse the wave function by putting a detector in the barrier and get a count? What properties does matter have in this state?

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    $\begingroup$ If you have found the particle in the barrier, then you must have just measured its position. This means that the particle is now in a state which is localised in position and consequently it does not have a well defined momentum $\endgroup$ – By Symmetry Feb 6 '17 at 16:58
  • $\begingroup$ How much does this differ from the case of bound state? A particle's energy is below it's rest mass and you just need some energy to kick it to another state. $\endgroup$ – jaromrax Feb 6 '17 at 17:16
  • $\begingroup$ @Symmetry, but you could have a well-enough defined momentum for the question to still be completely valid. Your detectors' position measurement can have a very large uncertainty for a large-enough barrier. $\endgroup$ – user1247 Jun 1 '17 at 16:31

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