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1 Ideal Quantum Gases independent particles: plane wave states with Fermions: Pauli prinziple, i.e. at most one particle per state Bosons: unlimited number of particles per state grand canonical ensemble for practical reasons geometric series fugacity: 2 Ideal Quantum Gases equations of state note: general relation for mono-atomic ideal gases particle number Fermi-Dirac distribution Bose-Einstein distribution Ideal Quantum Gases Fermions 3 spin multiplicity thermal wave length Ideal Quantum Gases Fermions 4 high-temperature / low-density limit fix particle density pressure insert increased pressure classical ideal gas quantum correction compressibility reduced because Fermions avoid each other Fermions 5 Ideal Quantum Gases high-temperature / low-density limit internal energy heat capacity classical quantum quantum note: 3rd law of thermodynamics Fermions 6 Ideal Quantum Gases low-temperature / high-density limit pz T=0: ground state pF occupied states py px particle density: Fermi energy Fermi momentum internal (ground state) energy: zero-piont pressure: Ideal Quantum Gases low-temperature / high-density limit T > 0: approximation particle density: Fermions 7 Fermions 8 Ideal Quantum Gases low-temperature / high-density limit T > 0: pressure internal energy: quantum note:
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