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Lecture_26 - PHYS 342 Fall 2011 Lecture 26: Quantum Gas Ron...

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PHYS 342 Fall 2011 Lecture 26: Quantum Gas on Reifenberger Ron Reifenberger Birck Nanotechnology Center Purdue University Lecture 26 1
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Important difference between classical and quantum statistics In classical mechanics: identical objects can be distinguished two identical balls can be labeled (marked) so that they can be distinguished from each other he position of an object in a system of identical objects can be known the position of an object in a system of identical objects can be known at any given time In quantum mechanics: identical particles cannot be labeled you know the probable position of two particles at some initial time you know the probable position of those two particles later in time annot determine which particle went where cannot determine which particle went where this property of very small particles is called Indistinguishability 2
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For two identical particles, the wave nature of quantum mechanics prevents us from determining which of the many article 1 article 2 article 2 article 1 possibilities actually occurred Particle 1 Particle 2 Particle 2 Particle 1 Particle 1 Particle 2 Particle 2 Particle 1 separation comparable to the de Broglie wavelength 3 1 click
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Important question: How to distinguish between a classical and quantum gas? wn n q u n u m g? Volume = V T s N= No. Particles Mass=m 3 13 () 4 4 N particle no n a v e r a ge s  Classical: 3 23 3 ,1 : 6.02 10 1 V s typically for mole at STP N Quantum: 3 25 3 3 22.4 0.001 3 2.7 10 / 4 n Vm molecules m s   2 2 2 2 3 22 B hp E pm h h T m k  4 2 sn m 1 click 3 B mk T 
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Expect classical gas when s >> λ Quantum gas avefunction overlap) Classical gas o wavefunction overlap) s >> λ s << λ s λ (wavefunction overlap) (no wavefunction overlap) 2 2 3 2 3 2 B B h kT mk T h m  from previous slide 1/3 3 , 4 also s n    3/2 ? 3 3 when is s mk T N  5 2 4 B when n Vh  
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Specific Examples s >> λ s << λ s λ electron 3 B h mk T  s ~ λ for T near 10K s << λ for low T (quantum gas) 1.0E+02 1.0E+03 gth (nm) H, He Ar N 2 1000 100 s >> λ for all T (classical gas) 1.0E+00 1.0E+01 wavelen g 10 1 s (for typical ideal gas at STP) 1.0E-02 1.0E-01 e Broglie =10K 0.1 0.01 s (for typical crystalline solid) .0E- 4 1.0E-03 thermal d e T=10K T=300K T=1000K 0.001 0.0001 6 1.0E 04 1.0E-31 1.0E-29 1.0E-27 1.0E-25 1.0E-23 1.0E-21 1.0E-19 Mass (kg)
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Consider a Collection of INDISTINGUISHABLE Particles Insights from Prior Energy Level Problem articles are now 9 6 Particles are now indistinguishable !
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Lecture_26 - PHYS 342 Fall 2011 Lecture 26: Quantum Gas Ron...

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