*Condensed Matter & Surface Sciences*

*COLLOQUIUM*

**ALEXANDER
V. CHAPLIK**

Russian
Academy of Sciences

*“**Quantum Generalization of the Thomas-Fermi Model**”*

The interaction between particles in the
mean-field approximation of the many-body theory is often taken into account
with the use of the semiclassical description of the
particle motion. However, quantization
of a part of the degrees of freedom becomes essential in certain cases. In this work, two such cases where nonlinear
wave equations appear have been considered: electrons in a quantum well and excitons in a
trap. In the case of indirect excitons
in an annular trap, the one-dimensional Gross–Pitaevskii
equation permits an analytical solution and it turns out that there can be no
bound state in a one-dimensional symmetric potential well. This makes the problem qualitatively different
from a similar one-body problem. In the
case of electrons in a quantum well, the nonlinear integro-differential
equation does not have an exact solution and the allowed energy levels have
been found by the direct variational method.

**Thursday, November 16, 2017**

4:10 p.m. -- Walter Lecture Hall 245