The periods of Josephson oscillations for non-interacting BEC obtained via different methods. The red diamonds and black circles indicate the Josephson oscillations periods versus coupling strength Ω, obtained via the CGPEs [Eq. (5)] and decouple equations [Eqs. (7)] respectively. The purple line is obtained from the solution of the three-mode equation (14) in the linear regime, i.e. T = π/J. Other parameters: interaction strength g = 0, spatial separation x0 = 3.