We consider a charged particle confined in a one-dimensional rectangular double-well potential, driven by an external periodic excitation at frequency Ω and with amplitude A. We find that there is the regime of the parametric resonance due to the modulation of the amplitude A at the frequency ω_prm, which results in the change in the population dynamics of the energy levels. The analysis relies on the Dirac system of Hamiltonian equations that are equivalent to the Schrödinger equation. Considering a finite dimensional approximation to the Dirac system, we construct the foliation of its phase space by subsets F_ab given by constraints a ≤ N₀ ≤ b on the occupation probabilities N₀ of the ground state, and describe the tunneling by frequencies ν_ab of the system's visiting subsets F_ab. The frequencies ν_ab determine the probability density and thus the Shannon entropy, which has the maximum value at the resonant frequency ω = ω_prm. The reconstruction of the state-space of the system's dynamics with the help of the Shaw-Takens method indicates that the quasi-periodic motion breaks down at the resonant value ω_prm.