Analytical and statistical mechanics

Your learning path

1. 01

   Euler-Lagrange equations and constraints

   For L(q,qdot,t), stationarity of S=∫L dt with fixed endpoints yields d/dt(∂L/∂qdot)−∂L/∂q=0.

   Advanced university · Notes · 8 questions
2. 02

   Hamilton equations, phase space and Poisson brackets

   For a regular Lagrangian, p=∂L/∂qdot and H=p qdot−L after expressing qdot in terms of q,p,t.

   Advanced university · Notes · 8 questions
3. 03

   Canonical ensembles and partition functions

   For a system at inverse temperature β=1/(kBT), the canonical probability of a microstate of energy E is exp(−βE)/Z.

   Advanced university · Notes · 8 questions