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)
