At the present time the uniqueness of the
properties of hydrogen-type systems (excitons, small
impurity centers) in thin semiconductor films is widely
recognized [1 ]. Firstly this uniqueness is due to the
fact, that in definite conditions the nature of the
center's internal interaction between the particles
becomes two-dimensional Columbic [2]. Under these
conditions the conventional approximate approach in the
theory of diamagnetic excitons (see e.g., [3]) becomes
inapplicable while studying hydrogen-type systems in
QWS structures in the case when a strong external
magnetic field is perpendicular to the film's plane. The
peculiarity of the current problem is in the fact that
as the Columbic internal interaction as well as the
interaction with the external magnetic field takes place
in the film's plane and at the direction of the size
quantization only the film's potential acts.
In the present work the hydrogen-type system is studied by
means of variation technique without any limiting
restrictions on the value of the magnetic field.
By means of two variation parameters the wave function and
the energy of the ground state are obtained. The evolution
of wave-function is studied in a wide range of magnetic
field's changeover. It is shown, that in the case of extreme
strong fields the system is described by means of Landau
states, while in the case of extreme weak fields --- by means
of the states of a hydrogen-type center. In the case of
moderate fields the state of system is considered to be a
peculiar symbiosis of the two extreme cases.
References:
1. V. V. Mitin, V. A. Kochelap,
M. A. Struscio. Quantum
Heterostructures. Microelectronics and
Optoelectronics. Cambridge University Press. 1999.
2 L. V. Keldish Letters to JETP v. 29, p. 716, (1979).
3. R. P. Seisyan. ``Spectroscopy of diamagnetic
excitons''. Moscow, Nauka PubHouse, 1984.
4. L. D. Landau, E. M. Lifshits. ``Quantum
Mechanics'', Moscow, Nauka Publ. House, 1974.