In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr’s correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume that the Fourier coefficients coincide for the case of large quantum number. We illustrate the procedure by analyzing the classical limit for the quantum harmonic oscillator and the particle in a box, although the method is quite general. We find, in an analytical fashion, the classical distribution arising from the quantum one as the zeroth order term in an expansion in powers of Planck’s constant. We interpret the correction terms as residual quantum effects at the microscopic-macroscopic boundary.

In this work we propose a model to analyze the interaction of a two-level atom (TLA) placed in a cross cavity configuration interacting with two electromagnetic fields injected within the cavity. A canonical transformation for field operators is proposed to obtain ef­fective Hamiltonian such as that of Jaynes-Cummings and we calculate the wave function via time-evolution operator. We present results for the atomic inversion for a state in the weak intensity regime.

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