What is particle under potential in quantum field theory? Let's say we solve the Schrodinger equation with infinite well. We can quantize the field by the resonance state and can get the annihilation and creation operator. So we will get the sort of particle corresponding to the resonance state. The resonance state would have mass corresponding to the energy and the mass will exist as the multiple of the minimum energy level.
Is the resonance state a new type of particle? If it's not, what does the creation operator create?
Let's consider we put a photon inside the infinite well. If the photon is not in the resonance state, the photon will be represented by the superposition of the resonance states. So when it goes inside the well, photon seems not a fundamental particle but a complex particle constructed from more basic states.
And if the resonance is the particle, what happens to the photon then? If we put a photon detection device inside the infinite well, can we detect the photon? Or is the photon's identity vanished completely and it's meanless to talk of the photon anymore?
 A: There is not one quantum field theory. One can use an infinite potential with a harmonic oscillator and create a theory of creation and annihilation operators, but to identify the mathematical  states with physical states, and in your question, particles, needs clear definitions.
With the  quantum field theory used in elementary particles, there are no infinite well solutions. The quantum fields are the free particle solutions of the corresponding equations, no potentials. For electrons it is the Dirac equation, for the photons it is the quantized Maxwell. Creation operators work in these plane wave functions, as well as annihilation operators, and that is how the Feynman diagrams for the interactions are decided upon and then calculated.
Potential wells  are another use of quantum field theory. but not for electrons and photons which are elementary particles. (BTW the physical solution of the Schrodinger equation energy levels for the hydrogen atom has the 1/r potential of the coulomb interaction.)
