Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations

Investigating Student Difficulties with Dirac Notation

Quantum mechanics is challenging even for advanced undergraduate and graduate students. Dirac notation is a convenient notation used extensively in quantum mechanics. We have been investigating the difficulties that the advanced undergraduate and graduate students have with Dirac notation. We administered written free response and multiple-choice questions to students and also conducted semi-structured individual interviews with 23 students using a think-aloud protocol to obtain a better understanding of the rationale behind their responses. We find that many students struggle with Dirac notat…

Student difficulties with representations of quantum operators corresponding to observables

Dirac notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum operators corresponding to observables especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students in advanced quantum mechanics courses. We discuss the analysis of data on the common difficulties found.

Student difficulties in translating between mathematical and graphical representations in introductory physics

We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution (a conducting sphere concentric with a conducting spherical shell) to 95 calculus-based introductory physics students. We asked students to write a mathematical expression for the electric field in various regions and asked them to graph the electric field. We knew from previous experience that studen…

利用多种表示形式提高学生对量子态的理解

Using multiple representations to improve student understanding of quantum states

本研究针对学生在量子态多种表示间转换的困难，开发并评估了量子交互式学习教程（QuILT），以提高学生的理解能力。

Student difficulties with determining expectation values in quantum mechanics

The expectation value of an observable is an important concept in quantum mechanics. However, upper-level undergraduate and graduate students in physics have both conceptual and procedural difficulties when determining the expectation value of physical observables, especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students. Here, we discuss the analysis of data on student difficulties when determining the expectation value.

用图形记号促进矢量微积分

Boosting Vector Calculus with the Graphical Notation

本文面向物理教学引入三维欧几里得矢量微积分的图形记号，通过展示教学优势和配套练习，降低学习门槛并帮助学生直观理解张量语言。