Hamburg 2001 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 13: Statistische Physik (Allgemein) II
DY 13.5: Vortrag
Montag, 26. März 2001, 11:30–11:45, S 7
Quantum Statistics of Hydrogen in Uniform Magnetic Field — •Michael Bachmann, Hagen Kleinert, and Axel Pelster — Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin
We extend the Feynman-Kleinert
variational approach [1] to find a single
approximation to the effective classical potential of hydrogen in uniform
magnetic field
for all temperatures and magnetic field strengths.
From this, the quantum statistical partition function is
obtained by a simple
configuration space integral over a classical-looking Boltzmann-factor.
In the zero-temperature limit, the effective classical potential
is the ground state energy of the system. For strong magnetic fields,
we obtain the dependence of the energy on the magnetic field strength B
consisting of various logarithmic terms which improve Landau’s famous
estimate (1/2)ln2 B [3].
[1] R.P. Feynman and H. Kleinert, Phys. Rev. A 34, 5080 (1986);
H. Kleinert,
Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics,
2nd ed. (World Scientific, Singapore, 1995).
[2] M. Bachmann, H. Kleinert, and A. Pelster, Phys. Rev. A 62, 52509
(2000).
[3] L.D. Landau and E.M. Lifschitz, Quantenmechanik, Sechste Auflage
(Akademie-Verlag, Berlin, 1979).