The main theme of our research program is to examine methodologies that differ from the standard "Oppenheimer-Schiff-Bohm" approach to quantum mechanics,
which is time-worn and does not work so well with students. This standard approach to quantum mechanics is based on a differential equation approach in the position-space basis.
This was a natural starting point when the paradigm was developed in the 1940s as a senior graduate-level course, but since then instruction moved earlier and earlier in our curriculum
(currently at the sophomore-level in the United States) and this approach needs to be rethought. Our research work has two main themes. The first is a focus on teaching
undergraduate quantum mechanics based on the approach commonly called Schrödinger's factorization method. We prefer to call this approach *Operator Mechanics* as an alternative
to matrix mechanics and wave mechanics. The other is based on Schrödinger's original solution to hydrogen, which employs the Laplace method for solving the Schrödinger
equation. This latter method also allows for one to teach complex analysis techniques along with quantum mechanics. It is more appropriate for graduate instruction.

Our research work is primarily involved with investigating different forms of pedagogy. Currently,
we are not involved in research on how well the new pedagogy works. While this is important, it is even more important to have new ideas for how to
teach quantum mechanics in this representation-independent format. Hopefully, we will be able to evaluate the efficacy of this work
in the future. *Any physics education researcher interested in collaborating with us on this should contact us directly.*

We have given a number of research talks on our pedagogical work. A collection of these talks appears below.

Undergraduates are well positioned to participate in developing quantum mechanics pedagogy. They know what it was like to *not* understand material in a particular subject
and also are great at clarifying what helped them to eventually understand the material. We are parterning with undergraduates on a series of research projects. Any undergraduates interesting
in joining the effort should contact us to discuss further.

Since 2018, we have been engaged in what we call *deep citizen science*. This is a form of citizen science where the intent
is to write a research paper with the citizen as the lead author from the outset of the project. One should think of this as similar to senior theses
written with undergraduate students. Most citizen scientists have undergraduate degrees in a technical field. Those in the lifelong learner category
tend to be retired professionals (engineers, doctors, etc.). Advanced high school students can also perform similar work for well designed projects. In all cases, it is important to develop
problems that the citizen scientist can work on and to mentor them carefully to the completion of the project. We have found that quantum pedagogy projects often
work well with citizen scientists. In the listing below, we include all Citizen Scientists who are high school students or whom we met through engagement with various MOOCs.
Not all fall into the traditional citizen scientists category, but the point of citizen science is that it is always nontraditional!

If you are interested in becoming a deep citizen scientist, just contact us!