An approximate approach to the quantum well in the presence of electric field and BenDaniel–Duke boundary condition

Very few problems are analytically solvable in quantum mechanics. We present an analytical approximation to the expression for quantized energies of a semiconductor quantum well placed in a constant electric field. The system is studied under the influence of the BenDaniel–Duke boundary condition. We obtain approximated scaling laws to understand the exact numerical results obtained. We study the size dependence, field dependence and charge densities on the mass ratio of electron outside and inside the well. We relate the obtained results to quantum confinement Stark effect. The approach is suitable to discuss in an undergraduate classroom. (paper)