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Ideal Quantum Gases

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Lectures on Quantum Statistics

Part of the book series: Lecture Notes in Physics ((LNP,volume 953))

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Abstract

Planck’s theory of radiation which is the origin of quantum statistics, was semi-phenomenological based on concepts of electrodynamics, classical thermodynamics, and classical radiation theory.

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Notes

  1. 1.

    In English: “Translator’s note. In my opinion, Bose’s derivation of Planck’s formula is an important step forward. The method used here gives also the quantum theory of the perfect gas, as I will discuss elsewhere.”

  2. 2.

    In English: “Thermal equilibrium in the radiation field in the presence of matter.”

References

  • Anderson, M.H., J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell. 1995. Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor. Science 269: 198–201.

    Article  ADS  Google Scholar 

  • Bobrov, V.B., A.G. Zagorodny, and S.A. Trigger. 2015. Coulomb Potential of Interaction and Bose-Einstein Condensate. Low Temperature Physics 41: 1154–1163 (in Russian).

    Google Scholar 

  • Bogolyubov, N.N. 1991. Selected Works. Vol. II. Quantum and Classical Statistical Mechanics. New York: Gordon and Breach.

    Google Scholar 

  • Bohm, D., and D. Pines. 1951. A Collective Description of Electron Interactions I. Magnetic Interactions. Physics Review 82: 625–634.

    Article  ADS  MathSciNet  Google Scholar 

  • Bose, S.N. 1924a. Plancks Gesetz und Lichtquantenhypothese. Zeitschrift fr Physik 26: 178–181.

    Article  ADS  Google Scholar 

  • Bose, S.N. 1924b. Wärmegleichgewicht im Strahlungsfeld bei Anwesenheit von Materie. Zeitschrift fr Physik 27: 178–181.

    Article  ADS  Google Scholar 

  • Davis, K.B., M.O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, and W. Ketterle. 1995. Bose-Einstein Condensation in a Gas of Sodium Atoms. Physical Review Letters 75: 3969–3973.

    Article  ADS  Google Scholar 

  • DeWitt, H.E. 1961. Thermodynamic Functions of a Partially Degenerate, Fully Ionized Gas. Journal of Nuclear Energy, Part C Plasma Physics 2: 27–45.

    Article  ADS  Google Scholar 

  • DeWitt, H.E. 1962. Evaluation of the Quantum-Mechanical Ring Sum with Boltzmann Statistics. Journal of Mathematical Physics 3: 1216–1228.

    Article  ADS  MathSciNet  Google Scholar 

  • DeWitt, H.E. 1966. Statistical Mechanics of High-Temperature Quantum Plasmas Beyond the Ring Approximation. Journal of Mathematical Physics 7: 616–626.

    Article  ADS  MathSciNet  Google Scholar 

  • Debye, P. 1912. Zur Theorie der Spezifischen Wärmen. Annalen der Physik 39: 789–839.

    Article  ADS  Google Scholar 

  • Dirac, P.A.M. 1926. On the Theory of Quantum Mechanics. Proceedings of Royal Society London A: Mathematical, Physical and Engineering Sciences 112: 661–677.

    Article  ADS  Google Scholar 

  • Ebeling, W. 1985. Statistical Thermodynamics of Fluid Hydrogen at High Energy Density. Physica A 130: 587–596.

    Article  ADS  Google Scholar 

  • Ebeling, W., and D. Hoffmann. 2014. Eine Vorlage Einsteins in der Preußischen Akademie der Wissenschaften. Leibniz Online. http://www.leibnizsozietaet.de/wp-content/uploads/2014/12/EbelingHoffmann.pdf.

  • Ebeling, W., W.D. Kraeft, and D. Kremp. 1976. Theory of Bound States and Ionisation Equilibrium in Plasmas and Solids. Berlin: Akademie-Verlag.

    Google Scholar 

  • Ebeling, W., W.D. Kraeft, D. Kremp, and G. Röpke. 1986. Quantum Statistics of Coulomb Systems: Thermodynamic Functions and Phase Transitions. Physica 140a: 160–168.

    Article  ADS  Google Scholar 

  • Einstein, A. 1907. Die Plancksche Theorie der Strahlung und die Theorie der Spezifischen Wärme. Annals of Physics 22: 180–190.

    Article  Google Scholar 

  • Einstein, A. 1924. Quantentheorie des Einatomigen Idealen Gases. Sitzungsber. Preuss. Akad. Wiss. Phys.-math. Kl 22: 261–267.

    Google Scholar 

  • Einstein, A. 1925. Quantentheorie des Einatomigen Idealen Gases. Zweite Abhandlung. Sitzungsber. Preuss. Akad. Wiss. Phys.-math. Kl 23: 3–14.

    MATH  Google Scholar 

  • Fermi, E. 1926. Über die Wahrscheinlichkeit der Quantenzustände. Zeitschrift für Physik 26: 54–56.

    Article  ADS  Google Scholar 

  • Feynman, R.P. 1972. Statistical Mechanics. Reading, MA: Benjamin.

    Google Scholar 

  • Fick, E. 1981. Einführung in die Grundlagen der Quantentheorie. Leipzig: Akademischer Verlag.

    MATH  Google Scholar 

  • Fukushima, T. 2015. Precise and Fast Computation of Fermi-Dirac Integral of Integer and Half Integer Order by Piecewise Minimax Rational Approximation. Applied Mathematics and Computation 259: 708–729.

    Article  MathSciNet  Google Scholar 

  • Huang, K. 1963. Statistical Mechanics. New York: Wiley.

    Google Scholar 

  • Huang, K. 2001. Introduction to Statistical Physics. London: Taylor & Francis.

    MATH  Google Scholar 

  • Ichimaru, S. 1992. Statistical Plasma Physics. Redwood: Addison-Wesley.

    MATH  Google Scholar 

  • Kirsten, C., and H.G. Körber, eds. 1975. Physiker über Physiker. Berlin: Akademie-Verlag.

    Google Scholar 

  • Klimontovich, Yu. L. 1982. Statistical Physics. Moscow: Nauka (in Russian).

    Google Scholar 

  • Kraeft, W.D., D. Kremp, W. Ebeling, and G. Röpke. 1986. Quantum Statistics of Charged Particle Systems. Berlin: Akademie-Verlag.

    Book  Google Scholar 

  • Kremp, D., M. Schlanges, and W.D. Kraeft. 2005. Quantum Statistics of Nonideal Plasmas. Berlin: Springer.

    MATH  Google Scholar 

  • Landau, L.D., and E.M. Lifshitz. 1976. Statistical Physics (Part I). Moscow: Nauka.

    Google Scholar 

  • Landau, L.D., and E.M. Lifshitz. 1980. Statistical Physics. Oxford: Butterworth-Heinemann.

    MATH  Google Scholar 

  • Landau, L.D., and E.M. Lifshitz. 1990. Statistical Physics. New York: Pergamon.

    MATH  Google Scholar 

  • Lether, F.G. 2000. Analytical Expansions and Numerical Approximations of Fermi-Dirac Integrals Fj(x) of Order j = −1 = 2 and j = 1∕2. Journal of Science Communication 15: 479–497.

    MathSciNet  MATH  Google Scholar 

  • Mayer, J.E. 1950. The Theory of Ionic Solutions. The Journal of Chemical Physics 18: 1426–1436.

    Article  ADS  Google Scholar 

  • Pauli, W. 1925. Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren. Zeitschrift für Physik 31: 765–783.

    Article  ADS  Google Scholar 

  • Petrich, W., M.H. Anderson, J.R. Ensher, and E.A. Cornell. 1995. Stable, Tightly Confining Magnetic Trap for Evaporative Cooling of Neutral Atoms. Physical Review Letters 74: 3352–3355.

    Article  ADS  Google Scholar 

  • Pines, D. 1963. Elementary Excitations in Solids. Lecture Notes and Supplements in Physics. New York: Benjamin.

    MATH  Google Scholar 

  • Pines, D., and P. Nozieres. 1966. The Theory of Quantum Liquids. New York: Benjamin.

    MATH  Google Scholar 

  • Riemann, B. 1859. Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse. Monatsberichte der Berliner Akademie, 671–680.

    Google Scholar 

  • Toda, M., R. Kubo, and N. Saito. 1983. Statistical Physics. Vols. I and II. Berlin: Springer.

    MATH  Google Scholar 

  • Treder, H.J. 1983. Große Physiker und ihre Probleme – Studien zur Geschichte der Physik. Berlin: Akademie Verlag.

    MATH  Google Scholar 

  • Zimmermann, R. 1988. Many Particle Theory of Highly Excited Semiconductors. Leipzig: Teubner.

    Google Scholar 

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Ebeling, W., Pöschel, T. (2019). Ideal Quantum Gases. In: Lectures on Quantum Statistics. Lecture Notes in Physics, vol 953. Springer, Cham. https://doi.org/10.1007/978-3-030-05734-3_3

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