The Quantum Well in an Electric Field A Density of States Approach

A quantum well (QW) in the presence of a homogeneous electric field forms a system with continuous energy spectrum. Its density of states (DOS) is calculated. A general DOS formula is applied which avoids the well‐known difficulties for systems with continuous spectra. The Schrödinger equation is solved exactly, and the 1D DOS is expressed in closed analytical form by means of Airy functions of first and second kind. Quasistationary energy levels are defined as zeros of a certain 4 × 4 matrix. Their positions are calculated in dependence on the field strength over a wide range. The 1D DOS peaks arising from quasistationary levels are studied for different field strengths. The same is done for the 1D DOS in a larger energy interval ranging from far below the QW bottom up to far above the QW barriers. Franz‐Keldysh oscillations as well as QW interferences are observed above the barriers.