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One obvious consequence of any finite potential is that a high enough energy wave-function will not form a bound state, either they are high enough energy they will generally just bypass the barrier or they can just tunnel through anyways. However, I was wondering if there were any methods by which you could create a bound state (or at least a loosely bound state) if you had some kind of high energy target frequency (lets say 1MeV) you wanted to trap?

Essentially I'm already familiar with the idea and mathematics of creating bound states and highly suspect you could create a potential that would allow you to exploit interferences such that you can create a region where almost you're entire probability density can be pinpointed to. I'm mainly curious how things change at higher frequencies and if you can kind of beat nature at her own game with human technology or if the high energy requirements make the engineering of a system to exploit this impossible. This same question also applies to heavy electrons, and (if possible) neutrons.

Is it possible to create a potential where, even though we have these very high energy states, you can "trap" a band of frequencies and make it very unlikely for these trapped frequencies to escape you potential?

Let's say you just needed to trap 1 MeV photons or some narrow band of frequencies around 1MeV, you don't really care what else gets through but here your specific goal is to keep those 1MeV photons from leaving the box.

EDIT: Since there has been a bit of confusion as to what I mean by a bound state, I'd like to elaborate.

By a bound state I'm simply referring to the energy levels in which your wavefunction is literally bound in a region of space. The classical examples being the particle in a box or the harmonic oscillator (pictured below)

enter image description here

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  • $\begingroup$ A "bound state" for a high energy charged particle state is called a "storage ring". The largest, highest energy storage ring made by humans is called LHC. It can hold 7TeV protons and approx. 1.6TeV per nucleon for heavy ions. Natural fields can bind higher energies. It is a little more complicated for photons which need mirrors. We have very good mirrors for visible light and we can make poor mirrors for low energy x-rays, above that it becomes a little questionable to talk about "bound states" for photons, unless you are happy with confinement of a photon gas by absorption and re-emission. $\endgroup$ – CuriousOne May 30 '15 at 5:46
  • $\begingroup$ Can you flesh out what exactly you mean by absorption and re-emission. How localized is the confinement? $\endgroup$ – Skyler May 30 '15 at 5:54
  • $\begingroup$ Skyler, I'm not quite clear what you're asking, but check out the Breit-Wheeler process. When you make a bound state with gamma rays, it's called pair production. Check out gamma-gamma physics. The electron itself is a "bound state", as is the positron. Annihilation unbinds them. $\endgroup$ – John Duffield May 30 '15 at 13:21
  • $\begingroup$ Examples may be the interiors of stars (it takes millions of years for photons to "escape" the core of the sun) or the gamma rays inside the casing of a thermonuclear weapon. Those are not "the same" photons, of course, but that's a problematic term to begin with in quantum field theory. $\endgroup$ – CuriousOne May 30 '15 at 14:20
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    $\begingroup$ that's why I'm asking if there are other tricks to get a bound state with these potentials, even if it isn't perfectly bound (since it can always tunnel through the barrier into somewhere else in the universe outside the apparatus). I feel like there should experimental methods to cause interference so that the wavefunction has a very low chance of leaking outside your experiment. I'll adjust the question a bit more. $\endgroup$ – Skyler May 31 '15 at 0:47

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