Developed by: Steven Pollock, Stephen Goldhaber, and many others in the University of Colorado Boulder PER group and physics department

**Level**

middle schoolhigh schoolintro collegeinter-mediateupper levelgrad school other

**Topics**

**Setting**

### Overview

**What?** Supplementary activities for upper-level Quantum I. Includes learning goals, interactive lectures, homework problems, student difficulties, tutorials, in-class group activities, and clicker questions. All materials are modular and can be mixed and matched with other teaching strategies or materials.

### Classroom video

### Student skills developed

**Designed for:**

- Conceptual understanding
- Problem-solving skills
- Using multiple representations

**Can be adapted for:**

- Making real-world connections
- Metacognition

### Instructor effort required

- Medium

### Resources required

- TAs / LAs
- Clickers / polling method
- Projector

### Resources

**Developer's website:**CU Upper-Division QM Curriculum

### Teaching Materials

You can download all course materials for free, including lecture slides, clicker questions, homework, exams, and solutions from the developer's website (you'll need to ask for a password to access solutions).

You can download course materials for an updated version of the course, using a spins first approach, from the Adaptable Curricular Exercises for Quantum Mechanics page on PhysPort.

### Research

**RESEARCH VALIDATION**

**Bronze Validation**

This is the third highest level of research validation, corresponding to:

- at least 1 of the "based on" categories
- at least 1 of the "demonstrated to improve" categories
- at least 1 of the "studied using" categories

### Research Validation Summary

#### Based on Research Into:

- theories of how students learn
- student ideas about specific topics

#### Demonstrated to Improve:

- conceptual understanding
- problem-solving skills
- lab skills
- beliefs and attitudes
- attendance
- retention of students
- success of underrepresented groups
- performance in subsequent classes

#### Studied using:

- cycle of research and redevelopment
- student interviews
- classroom observations
- analysis of written work
- research at multiple institutions
- research by multiple groups
- peer-reviewed publication

### References

- G. Corsiglia, T. Garcia, B. Schermerhorn, G. Passante, H. Sadaghiani, and S. Pollock, Characterizing and monitoring student discomfort in upper-division quantum mechanics, presented at the Physics Education Research Conference 2020, Virtual Conference, 2020.
- G. Corsiglia, S. Pollock, and B. Wilcox, Effectiveness of an online homework tutorial about changing basis in quantum mechanics, presented at the Physics Education Research Conference 2022, Grand Rapids, MI, 2022.
- M. Dubson, S. Goldhaber, S. Pollock, and K. Perkins, Faculty Disagreement about the Teaching of Quantum Mechanics, presented at the Physics Education Research Conference 2009, Ann Arbor, Michigan, 2009.
- S. Goldhaber, S. Pollock, M. Dubson, P. Beale, and K. Perkins, Transforming Upper-Division Quantum Mechanics: Learning Goals and Assessment, presented at the Physics Education Research Conference 2009, Ann Arbor, Michigan, 2009.
- I. Hanemann, J. Hoehn, and N. Finkelstein, Characterizing differences in students' epistemologies between classical and quantum physics, presented at the Physics Education Research Conference 2018, Washington, DC, 2018.
- J. Meyer, G. Passante, S. Pollock, M. Vignal, and B. Wilcox, Investigating studentsâ€™ strategies for interpreting quantum states in an upper-division quantum computing course, presented at the Physics Education Research Conference 2021, Virtual Conference, 2021.
- J. Meyer, G. Passante, S. Pollock, and B. Wilcox, Investigating student interpretations of the differences between classical and quantum computers: Are quantum computers just analog classical computers?, presented at the Physics Education Research Conference 2022, Grand Rapids, MI, 2022.
- G. Passante, P. Emigh, and P. Shaffer, Testing Tutorials in Upper-Division: An Example from Quantum Mechanics, presented at the Physics Education Research Conference 2014, Minneapolis, MN, 2014.
- K. Perkins and C. Turpen, Student Perspectives on Using Clickers in Upper-division Physics Courses, presented at the Physics Education Research Conference 2009, Ann Arbor, Michigan, 2009.
- S. Pollock, S. Chasteen, M. Dubson, and K. Perkins, The use of concept tests and peer instruction in upper-division physics, presented at the Physics Education Research Conference 2010, Portland, Oregon, 2010.
- S. Pollock, H. Sadaghiani, A. Quaal, and G. Passante, Designing, validating, and contrasting conceptual quantum mechanics questions for spin states and spatial wave functions, presented at the Physics Education Research Conference 2018, Washington, DC, 2018.
- S. Pollock and B. Wilcox, Upper-Division Students' Use of Separation of Variables, presented at the Physics Education Research Conference 2015, College Park, MD, 2015.
- H. Sadaghiani, J. Miller, S. Pollock, and D. Rehn, Constructing a Multiple-choice Assessment for Upper-division Quantum Physics from an Open-ended Tool, presented at the Physics Education Research Conference 2013, Portland, OR, 2013.
- H. Sadaghiani, G. Passante, and S. Pollock, Student understanding of quantum mechanical expectation values in two different curricula, presented at the Physics Education Research Conference 2018, Washington, DC, 2018.
- H. Sadaghiani and S. Pollock, Quantum mechanics concept assessment: Development and validation study, Phys. Rev. ST Phys. Educ. Res.
**11**(1), 010110 (2014). - B. Schermerhorn, A. Villasenor, D. Agunos, H. Sadaghiani, G. Passante, and S. Pollock, Student perceptions of math-physics interactions throughout spins-first quantum mechanics, presented at the Physics Education Research Conference 2019, Provo, UT, 2019.
- J. Wells, H. Sadaghiani, B. Schermerhorn, S. Pollock, and G. Passante, Deeper look at question categories, concepts, and context covered: Modified module analysis of quantum mechanics concept assessment, Phys. Rev. Phys. Educ. Res.
**17**(2), 020113 (2021). - B. Wilcox, M. Caballero, C. Baily, H. Sadaghiani, S. Chasteen, Q. Ryan, and S. Pollock, Development and uses of upper-division conceptual assessments, Phys. Rev. ST Phys. Educ. Res.
**11**(2), 020115 (2015). - B. Wilcox and S. Pollock, Upper-division student difficulties with the Dirac delta function, Phys. Rev. ST Phys. Educ. Res.
**11**(1), 010108 (2015).