Warm-Up (Welcome Activity Reviewing Material from Undergraduate Physics)

This content is used in the Physics Department at OSU with incoming graduate students to remind them of undergraduate content before classes start and to help them to decide whether or not to take some Bridge Courses. This sequence is intended to run in two blocks of three hours each. The sessions should be run by someone with a deep knowledge of all of the relevant courses, the specific activities, and active engagement in general.

This session may be the first opportunity for the incoming graduate students to meet each other as well as some faculty and other graduate students. So start with a 1/2 hour dedicated to introductons.

Consider inviting some or all of the following people to participate:

  • At least one faculty member to run the session who has broad experience with the curriculum and the activities--typically the Paradigms Director.
  • Graduate students who have TAd for courses that incorporated these exact activities, as needed to provide one experienced person to sit with each group of three graduate students. The Head Graduate Advisor has often asked these graduate students for evaluative input regarding the members of their group. CAM thinks that they should be given a heads-up about what will be expected.
  • The Head Graduate Advisor (n.b. In the past the Grad Advisor has roamed the classroom, hovering over the groups as they work. CAM thinks this can appear intimidating/judgmental. Consider asking the grad advisor to SIT with groups, even if they move frequently from group to group.
  • Members of the Core Advising Committee
  • Faculty who will be teaching the Bridge Courses so that they are available to answer student questions, especially individual questions during breaks.
  • Graduate students who have take Bridge Courses in the past who are comfortable discussing their choices and experiences.

1. Activity: Warm-Up Powerpoint
Discuss the possible paths for graduate students using the attached powerpoint. Make sure to use neutral language: Bridge Courses and Core Courses.
The attached powerpoint articulates the possible paths through the curriculum for new graduate students at OSU. Make sure to update this powerpoint yearly to reflect current course offerings and sequencing. It was partially, but not completely edited in fall 2022.
2. Activity: Representations of the Infinite Square Well
This activity is used to help students self-assess their knowledge of quantum mechanics at the level of Griffiths QM. Related bridge courses are: PH 425 (Quantum Fundamentals, particularly valuable if students have not seen bra/ket notation), PH 426 (Central Forces, includes PDEs and separation of variables), PH 427 (Periodic Systems, includes both the free particle and an introduction to solid state), PH 451 (Capstone in Quantum Mechanics, a great course for students from small schools who have not studied perturbation theory). Note that the graduate quantum sequence covers all quantum topics from the beginning, but at a fast pace; so students who are missing content but feel that they can handle the pace can be successful without taking bridge courses.
3. Activity: Changes in Internal Energy (Remote)
This activity is used to help students self-assess their knowledge of thermodynamics. Briefly discuss the difference between thermodynamics and statistical mechanics and how that content is distributed in the bridge course choices, PH 423 (Energy and Entropy--mostly thermodynamics) and PH 441 (Capstone in Statistical Mechanics--mostly statistical mechanics) vs. the graduate sequence PH 641/2.
Students consider the change in internal energy during three different processes involving a container of water vapor on a stove. Using the 1st Law of Thermodynamics, students reason about how the internal energy would change and then compare this prediction with data from NIST presented as a contour plot.
4. Activity: Electrostatic Potential Due to a Point Charge
This small whiteboard question is an essential prerequisite to the Electrostatic Potential Due to a Ring, which follows immediately in this sequence. This is a great opportunity to discuss the potential role of small whiteboards in their own teaching.
5. Activity: Electrostatic Potential Due to a Ring of Charge
This activity is used to help students self-assess their knowledge of electrostatics at the level of Chapter 2 of Griffiths. Related bridge courses are PH 422 (Static Fields) and PH 431 (E and M Capstone). If there is time, have groups try one of the power series expansions (e.g. \(s<<R\)) as an assessment of whether they should take PH 561 (Graduate Math Methods).

Students work in small groups to use the superposition principle \[V(\vec{r}) =\frac{1}{4\pi\epsilon_0}\int\frac{\rho(\vec{r}^{\,\prime})}{\vert \vec{r}-\vec{r}^{\,\prime}\vert} \, d\tau^{\prime}\] to find an integral expression for the electrostatic potential, \(V(\vec{r})\), everywhere in space, due to a ring of charge.

In an optional extension, students find a series expansion for \(V(\vec{r})\) either on the axis or in the plane of the ring, for either small or large values of the relevant geometric variable. Add an extra half hour or more to the time estimate for the optional extension.