Harmonic oscillator model for the atom-surface Casimir-Polder   interaction energy
  In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting plate. Using an appropriate Bogoliubov-type transformation we can diagonalize exactly the Hamiltonian of our system in the continuum limit and obtain non-perturbative expressions for its ground-state energy. From the expressions found, the atom-wall Casimir-Polder interaction energy can be obtained, and well-know lowest-order results are recovered as a limiting case. Use and advantage of this method for dealing with other systems where perturbation theory cannot be used is also discussed. 
Roberto Passante, Lucia Rizzuto, Salvatore Spagnolo, Satoshi Tanaka,   Tomio Y. Petrosky
quant-ph