Condensed Matter Physics, 2006, vol. 9, No. 4(48), p.645-658, English

Title: Quantum statistical mechanics of electron gas in magnetic field
  I.M.Dubrovskii (Institute for Metal Physics, 36 Academician Vernadsky Blvd., Kyiv--142, 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 two-dimensional 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

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