Transcription of 8.044 Lecture Notes Chapter 9: Quantum Ideal Gases
{{id}} {{{paragraph}}}
Example: barber
8.044 Lecture Notes Chapter 9: Quantum Ideal Gases
Lecture Notes Chapter 9: Quantum Ideal Gases Lecturer: McGreevy Range of validity of classical Ideal gas .. 9-2. Quantum systems with many indistinguishable particles .. 9-4. Statistical mechanics of N non-interacting (indistinguishable) bosons or fermions 9-9. Classical Ideal gas limit of Quantum Ideal gas .. 9-13. Ultra-high temperature (kB T mc2 and kB T ) limit .. 9-15. Fermions at low temperatures .. 9-18. Bosons at low temperatures .. 9-33. Reading: Baierlein, Chapters 8 and 9. 9-1. Range of validity of classical Ideal gas For a classical Ideal gas, we derived the partition function 3/2. Z1N.. V 2 mkB T. Z= , Z1 = 3 = V , N! th h2. h where the length scale th 2 mkB T. is determined by the particle mass and the temperature. When does this break down? 1. If idealness' fails, if interactions become important. This is interesting and impor- tant but out of bounds for We'll still assume non-interacting particles. 2. If classicalness' fails. Even with no interactions, at low enough temperatures, or high enough densities, Quantum effects modify Z.
9.2 Quantum systems with many indistinguishable particles [This section is about quantum mechanics. You’ve already encountered some of these ideas in 8.04, and will discuss this further in 8.05. We’ll come back in subsection 9.4 and think about when this business reduces to classical mechanics.] Consider two particles.
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: