Exact transmission state of a Bose–Einstein condensate in a near-harmonic trap

We introduce a new confining potential which simulates preferably the realistic near-harmonic trap for a quasi-one-dimensional (1D) Bose–Einstein condensate (BEC). An exact transmission state of the BEC system is found and the corresponding spatial configurations, metastability, superfluidity and the transport properties are analyzed. Resonant transmission through the potential is predicted from the exact solution.