1: Classical mechanics
- Page ID
- 426698
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- 1.1: The Lagrangian Formulation of Classical Mechanics
- In order to begin to make a connection between the microscopic and macroscopic worlds, we need to better understand the microscopic world and the laws that govern it. We will begin placing Newton's laws of motion in a formal framework which will be heavily used in our study of classical statistical mechanics.
- 1.2: The Hamiltonian formulation of classical mechanics
- The Lagrangian formulation of mechanics will be useful later when we study the Feynman path integral. For our purposes now, the Lagrangian formulation is an important springboard from which to develop another useful formulation of classical mechanics known as the Hamiltonian formulation. The Hamiltonian of a system is defined to be the sum of the kinetic and potential energies expressed as a function of positions and their conjugate momenta.
- 1.4: Phase Space
- We construct a Cartesian space in which each of the 6N coordinates and momenta is assigned to one of 6N mutually orthogonal axes. Phase space is, therefore, a 6N dimensional space. A point in this space is specified by giving a particular set of values for the 6N coordinates and momenta.
- 1.6: Phase space distribution functions and Liouville's theorem
- Given an ensemble with many members, each member having a different phase space vector x corresponding to a different microstate, we need a way of describing how the phase space vectors of the members in the ensemble will be distributed in the phase space.