The electronic states of a core/shell quantum well (QW) system confined in a modified Pöschl–Teller (PT) plus Woods–Saxon (WS) potential in the presence of electric field are studied with the III-Nitride group owing to their wide bandgap for device applications. The bandgap energy in this regard is obtained by solving analytically the Schrödinger wave equation with the Pekeris-type approximation to the centrifugal term.