CRC Press eBooks

Ensembles, Energy Levels, and Microstates

Jonathan Allday, Simon Hands

Published Sep 3, 2024• 0 citations

Abstract

In the previous chapter, we set up a basic framework for exploring thermodynamics in a quantum regime. We have seen that constrained particles “in a box” have quantized energies (energy levels) specified by a quantum number that helps us to index microstates. Under appropriate and limited circumstances, we can model work done by a change in the energy values of the different levels while heating the system shuffles the pack in terms of the probability for occupying the levels. In this chapter, we proceed to fill in some vital details. The idea of an ensemble is formalized, and two of the key examples explored. We also derive the Boltzmann distribution in two complementary ways. Finally, we turn the quantum version of an ideal gas, and in the process derive a formula for the entropy. Our first task, however, is to discuss the issues pertinent to our ability to count microstates .

DOI: 10.1201/9781003121053-10

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