| dbo:abstract |
The results of the quantum harmonic oscillator can be used to look at the equilibrium situation for a quantum ideal gas in a harmonic trap, which is a harmonic potential containing a large number of particles that do not interact with each other except for instantaneous thermalizing collisions. This situation is of great practical importance since many experimental studies of Bose gases are conducted in such harmonic traps. Using the results from either Maxwell–Boltzmann statistics, Bose–Einstein statistics or Fermi–Dirac statistics we use the Thomas–Fermi approximation (gas in a box) and go to the limit of a very large trap, and express the degeneracy of the energy states as a differential, and summations over states as integrals. We will then be in a position to calculate the thermodynamic properties of the gas using the partition function or the grand partition function. Only the case of massive particles will be considered, although the results can be extended to massless particles as well, much as was done in the case of the ideal gas in a box. More complete calculations will be left to separate articles, but some simple examples will be given in this article. (en) |
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dbr:Quantum_harmonic_oscillator dbr:Bose–Einstein_statistics dbc:Statistical_mechanics dbr:Chemical_potential dbr:Gas_in_a_box dbr:Partition_function_(statistical_mechanics) dbr:Temperature dbr:Bose_gas dbr:Polylogarithm dbr:Fermi_gas dbr:Fermi–Dirac_statistics dbr:Maxwell–Boltzmann_statistics dbr:Boltzmann's_constant dbr:Equilibrium_solution dbr:Grand_partition_function dbr:Thomas–Fermi_approximation |
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dbc:Statistical_mechanics |
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The results of the quantum harmonic oscillator can be used to look at the equilibrium situation for a quantum ideal gas in a harmonic trap, which is a harmonic potential containing a large number of particles that do not interact with each other except for instantaneous thermalizing collisions. This situation is of great practical importance since many experimental studies of Bose gases are conducted in such harmonic traps. (en) |
| rdfs:label |
Gas in a harmonic trap (en) |
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freebase:Gas in a harmonic trap wikidata:Gas in a harmonic trap https://global.dbpedia.org/id/4k9ai |
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wikipedia-en:Gas_in_a_harmonic_trap?oldid=964041473&ns=0 |
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wikipedia-en:Gas_in_a_harmonic_trap |
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dbr:Quantum_harmonic_oscillator dbr:Index_of_physics_articles_(G) dbr:Gas_in_a_box dbr:Bose_gas |
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wikipedia-en:Gas_in_a_harmonic_trap |