Condensed Matter Physics, 2006, vol. 9, No. 4(48), p.645658, English
DOI:10.5488/CMP.9.4.645
Title:
Quantum statistical mechanics of electron gas in
magnetic field
Author(s):
 I.M.Dubrovskii
(Institute for Metal Physics,
36 Academician Vernadsky Blvd., Kyiv142, 03680, Ukraine)

Electron eigenstates in a magnetic field are considered. Density
of the probability current and an averaged magnetic moment are
obtained. Density of states is investigated for twodimensional
electron in a circle that is bound by the infinite potential
barrier. The present study shows that the common quantum
statistical mechanics of electron gas in a magnetic field leads to
incorrect results. The magnetic moment of electron gas can be
computed as the sum of averaged moments of the occupied states.
The computations lead to the results that differ from the ones
obtained as the derivative of the thermodynamical potential with
respect to the magnetic field. Other contradictions in common
statistical thermodynamics of electron gas in a magnetic field are
pointed out. The conclusion is done that these contradictions
arise from using the incorrect statistical operator. A new quantum
function of distribution is derived from the basic principles,
taking into account the law of conservation of an angular
momentum. These results are in accord with the theory that has
been obtained within the framework of classical statistical
thermodynamics in the previous work.
Key words:
electron states, magnetic field, angular momentum,
averaged magnetic moment, quantum function of distribution,
quantum statistical thermodynamics
PACS:
05.30.Ch, 75.20.g
