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Maximizing the Lagrangian

Keywords: Energy and Entropy, Thermo & Stat Mech, Quantum Physics, Eigenvalues, Probability, Small Group Activity


Highlights of the activity

  1. This small group activity is designed to give students practice with maximizing Lagrangians.
  2. Students use what they know to maximize the Lagrangian and derive additional information about the probability for any arbitrary state in the system as well as the partition function.
  3. The whole class discussion focuses on ensuring that students understand the steps required to maximize the Lagrangian.

Reasons to spend class time on the activity

For many students, this activity may be the first time they are seeing a Lagrangian. This activity demonstrates the usefulness of the method of Lagrange Multipliers to acquire additional information about a system. This activity also provides students the opportunity to manipulate the fairness function. Having small groups perform this exercise will also transition into defining the partition function and how it's notation is used to simplify expressions.


Instructor's Guide

Authors: Corinne Manogue
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