THE DENSITY OF STATES IN THE CONTINUOUS-SPECTRUM OF ONE-DIMENSIONAL SYSTEMS

The change in the density of states introduced by some localized potential DELTArho(E) is finite even for infinite systems. We derive some simple analytical formulae for this quantity for three different one-dimensional systems: a finite potential step, a uniform electric field and a flat potential. In each case we relate DELTArho(E) to some parameters of the wavefunction. Our analytical expressions for DELTArho(E) should be useful in analysing the continuous spectrum of layered microstructures. As an example, we determine DELTArho(E) above the symmetric and asymmetric quantum wells.