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Lecture 18: Quantum Statistics and Applications
April 3, 2025
Reading Assignment
- Read: Supplementary Reading Ch 6
Objectives
- (Continuing objective) Describe applications of the concepts of quantum mechanics to everyday “real-life” situations.
- Construct two-particle states from single-particle states for classical, distinguishable particles, and for indistinguishable fermions and bosons. Show that two fermions cannot be in the same state and that bosons “like” to be in the same state.
- Match the two particle types (bosons or fermions) with their spin value (integer or \(1 \over 2\)-odd integer). Apply the Pauli exclusion principle to systems with multiple fermions and relate this principle to the Periodic Table of the Elements.
- Describe the basic properties of lasers, superconductors, and superfluids, and how these processes originate from bosons affinity for being in the same state. Describe stimulated emission and explain why a population inversion is necessary for the operation of a laser.
Homework
- Friday's Assigned Problems: Supp CH 6: 1, 2, 3, 4, 5, 6, 8, 10, 16
- Monday's Hand-In Problems from Lecture 18:
Supp CH 6: 11, 12, 13, 14, 15
Note: this is only the second half of the hand-in set.
Lecture Materials
- Click here for the Lecture overheads.
- PheT laser simulation. Click on the “Multiple Atoms (lasing)” tab and see what you need to do to get a working laser! (Hint: you need to play around with the lifetimes to get a reasonable population inversion.)
Videos of example problems
To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.- First part of long example of how to write two particle states. This part has distinguishable particles and identical bosons.
- Second part of long example of how to write two particle states. This part has identical fermions.
- Video Example with bosons and fermions in a particle-in-box systems.
Pre-Class Entertainment
- Moonshadow - Cat Stevens
- Under the Bridge - Red Hot Chili Peppers
- Stand - R.E.M.
- Better - Regina Spektor
- Ants Marching - Dave Matthews Band
Assigned Problems Guide
- Supp 6-1: quick, but subtle. This gets at the heart of indistinguishability.
- Supp 6-2: quick. Remember: different particle types are always distinguishable.
- Supp 6-3: medium. Practice making a table of possible states like we did in class. Use Fig. 6.1 as a reference.
- Supp 6-4: medium-short. Very much like the concept test of putting electrons into states. One difference here: you're asked for the total energy, not the energy of the highest energy particle.
- The rest is coming soon!