Statistical Comparison of Eigenvalues of a Disturbed Schrödinger Operator

In this paper we introduce Schrödinger's operators in a naive and unpretentious way, but with some precision and didactics. The most studied periodic and random potential types are mentioned and, by numerical simulation, compare the eigenvalues of an operator's truncated matrix with a periodic potential and the same potential disturbed by an evenly distributed continuous random variable. We evaluated the magnitude of the random variable required to produce a significant difference between the eigenvalue sets.

Keywords:
Schrödinger operators; periodic potential; disturbed potential