In this course, we will examine a mathematically tractable and physically useful problem - that of two bodies interacting with each other through a central force, i.e. a force that has two characteristics:
Definition of a Central Force:
The most common examples of this type of force are those that have \(\frac{1}{r^2}\) behavior, specifically the Newtonian gravitational force between two point (or spherically symmetric) masses and the Coulomb force between two point (or spherically symmetric) electric charges. Clearly both of these examples are idealizations - neither ideal point masses or charges nor perfectly spherically symmetric mass or charge distributions exist in nature, except perhaps for elementary particles such as electrons. However, deviations from ideal behavior are often small and can be neglected to within a reasonable approximation. (Power series to the rescue!) Also, notice the difference in length scale: the archetypal gravitational example is planetary motion - at astronomical length scales; the archetypal Coulomb example is the hydrogen atom - at atomic length scales.
The two solutions to the central force problem - classical behavior exemplified by the gravitational interaction and quantum behavior exemplified by the Coulomb interaction - are quite different from each other. By studying these two cases together in the same course, we will be able to explore the strong similarities and the important differences between classical and quantum physics.
Two of the unifying themes of this topic are the conservation laws:
In the classical mechanics case, we will obtain the equations of motion in three equivalent ways,
We will also consider forces that depend on the distance between the two bodies in ways other than \(\frac{1}{r^2}\) and explore the kinds of motion they produce.
face Lecture
120 min.
ideal gas particle in a box grand canonical ensemble chemical potential statistical mechanics
These notes from week 6 of Thermal and Statistical Physics cover the ideal gas from a grand canonical standpoint starting with the solutions to a particle in a three-dimensional box. They include a number of small group activities.assignment_ind Small White Board Question
30 min.
Angular Momentum Spin Magnetic Moment Stern-Gerlach Experiments
Students consider the relation (1) between the angular momentum and magnetic moment for a current loop and (2) the force on a magnetic moment in an inhomogeneous magnetic field. Students make a (classical) prediction of the outcome of a Stern-Gerlach experiment.face Lecture
30 min.
face Lecture
120 min.
Planck distribution blackbody radiation photon statistical mechanics
These notes from the fourth week of Thermal and Statistical Physics cover blackbody radiation and the Planck distribution. They include a number of small group activities.group Small Group Activity
120 min.
face Lecture
120 min.
Gibbs entropy information theory probability statistical mechanics
These lecture notes for the first week of Thermal and Statistical Physics include a couple of small group activities in which students work with the Gibbs formulation of the entropy.group Small Group Activity
30 min.
group Small Group Activity
30 min.
group Small Group Activity
30 min.
assignment Homework