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The allowed energies for a particle inside a potential well are discrete ones, and for a particle outside the well, the energy specrum is continuum. But what for a particle inside a potential barrier? Are there allowed values for the energy? And if there are, are they discrete or continuum?

Qmechanic
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Elismar Lösch
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  • see https://en.wikipedia.org/wiki/Electromagnetic_radiation#Electromagnetic_spectrum . Whether the energy eigenvakues are continuus or not It will depend on the boundary conditions . For real particles one has to use wavepackets anyway,. – anna v Jun 28 '19 at 16:47
  • Related: https://physics.stackexchange.com/q/11188/2451 and links therein. – Qmechanic Jun 30 '19 at 04:50

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So, if I understand it correctly, the context of the question is quantum tunneling. Well, in such a scenario the particle is actually forbidden inside the barrier. Hence, it does not have a spectrum there. What this means is that the propagation constant of a particle with a certain energy becomes imaginary inside the barrier and its wave function thus becomes a decaying exponential.

Analogous scenarios exist in classical physics. Consider for instance light being launched into an optical fibre while its frequency is below the cut-off of the fibre. Instead of propagating along the fibre, the light decays. That is because there is no band ("energy level") in the fibre at that frequency.

flippiefanus
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