TITLE:
Non Perturbative Approach to the Time Evolution of a Simple Excited Coupled Quantum System in a Cavity
AUTHORS:
Adolfo P.C. Malbouisson
KEYWORDS:
Radiation Process in Cavities, Dressed Coordinates
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.6,
June
30,
2022
ABSTRACT: We consider a system modeled by a harmonic oscillator of frequency , coupled to the scalar potential inside a reflecting sphere of radius R. We use dressed states introduced originally in [1] and recently employed in [2] to present a non-perturbative unified description of the decay process of the system, in free space and in the case of the system being confined in a finite cavity. In the situation that we start from the initial condition that the system is in the first excited state, we give exact formulas to describe its time evolution for a cavity of arbitrary size. In the particular case of a very large cavity (free space), we recover the behaviour expected from perturbation theory in the limit of the small coupling constant. In the case of a very small cavity, our results are in good agreement with experimental observations