### Book chapter

## On discrete WKB methods for resonance electromagnetic traps

We consider a model quantum Hamiltonian of a charge in a resonance electromagnetic trap. Using

the operator averaging method, we obtain an effective quantum operator that asymptotically describes

the anharmonic part of the Hamiltonian. We show that the operator becomes a second-order difference

operator in a specially chosen quantum action-angle representation. Using the discrete WKB method for

this difference equation, we obtain the semiclassical WKB asymptotics of the spectrum and stationary

states of the charge.

**Mathematical modeling of resonance systems**(2019)