One hundred years ago Werner Heisenberg proposed a new form of mechanics based on Bohr's 1913 theory of atoms, which very quickly led to the vibrant field of physics we know as quantum mechanics. A handful of novel and relatively simple concepts completely changed our understanding of nature. A few decades later, applications of quantum mechanics, such as semiconductors and lasers, revolutionized our world. Even today we are witnessing innovations based on these novel ideas, including applications of entanglement, which Erwin Schrödinger considered to be at the very core of quantum mechanics. Quantum mechanics still holds plenty to explore and still raises fundamental conceptual questions.
Over the past 100 years, our understanding and use of quantum mechanics have grown substantially. Numerous Nobel Prizes have been awarded for advances in the field, from how atoms are built up from constituents, to how solids conduct electricity, to how strange phase transitions may happen at sufficiently low temperatures, to the very basis of how to measure time to unprecedented accuracy using atoms. Simultaneously, the educational landscape of quantum science and technology has been changing rapidly, and quantum mechanical concepts are being introduced into secondary school curricula and public outreach activities.
In order to celebrate and reflect on the development of quantum mechanics, the United Nations has declared 2025 the International Year of Quantum Science and Technology. In this special issue, we join the celebration, showing how this field is relevant to our lives and especially to modern physics education. We hope to provide inspiration for how to celebrate it in your classrooms. Our contributors shared so many good ideas that we are printing papers from the special collection not only in this issue, but also in the February issue. The following is a brief description of the papers in this issue.
We begin, appropriately, with a consideration of how the language that we use to describe quantum mechanics developed and changed over time. In order to describe new phenomena, physicists had to adapt or invent language. Helge Kragh provides a historical-linguistic perspective to quantum mechanics on p. 7 discussing the origins and linguistic history of some of the terms we use in quantum mechanics, showing how the usage of some words came to be established in the field.
Following that introduction, several papers of this celebratory issue consider innovative approaches to our current quantum mechanics courses, both in class and in the teaching laboratory. Quantum mechanics is often introduced following Schrödinger's approach in which the state of the system is represented by a wavefunction, and matrix representation only emerges when spin is introduced. However, the use of matrices was a competing description at the birth of this new theory. Papers by J. Tran, L. Doughty, and J. K. Freericks (p. 14) and Elina Palmgren and Ricardo Karam (p. 21) share approaches to teaching matrix mechanics that help students understand how matrix mechanics developed and apply it to systems such as the harmonic oscillator. Alternatively, one may introduce quantum mechanics via systems with finite numbers of degrees of freedom. Gauthier Rey, Renaud Mathevet, Sébastien Massenot, and Benoit Chalopin (p. 28) provide a way to introduce quantum mechanics via analyzing a two-mode Mach-Zehnder interferometer. Frederick Strauch (p. 34) investigates decoherence, entanglement, and information in the double-slit experiment conducted with electrons, shedding light on the profound connection between quantum physics and information theory. Jeremy Levy and Chandralekha Singh (p. 46) present teaching materials used to cover Dirac's notation, operators, and the Born rule in introductory physics courses.
Teaching quantum mechanics is often challenging, making it important to check whether students understand and can apply the material. Ben Brown, Guangtian Zhu, and Chandralekha Singh (p. 52) scrutinized students’ understanding of time dependence of expectation values in quantum mechanics using an interactive tutorial on Larmor precession. The tutorials and assessment questions are shared with readers via supplementary material. Anastasia Lonshakova, Kyla Adams, and David Blair focused on how young students, aged 11-15, could gain and retain their knowledge of the concepts of quantum probability and quantum spin (p. 58). The progression of activities that were developed could be used in a range of outreach activities.
In celebrating the first hundred years of quantum mechanics it is natural to reflect on its birth, discuss its development, how we can teach its concepts and interpret its predictions. But it is also vital to see how it continues to develop and contemplate what the near future holds. We share several papers sharing ideas of how contemporary developments of quantum computation and communication can be introduced at a variety of levels: to the public, to secondary school students, or in introductory courses on quantum mechanics.
Pedro Neto Mendes, Paulo André, and Emmanuel Zambrini Cruzeiro present (p. 69) a quantum key distribution setup based on the BB84 protocol that can be used for science outreach, in the undergraduate laboratory, or in class demonstrations. Mark Hannum (p. 78) introduces Grover's search algorithm to high school students and shows the differences between classical and quantum search. Dominik Schneble, Tzu-Chieh Wei, and Angela Kelly report on a quantum information science and technology summer program for high school students on p. 88, in which essential classical physics concepts, such as waves and polarization, are introduced, and then lead to a carefully chosen series of quantum ideas leading through superposition, measurement, entanglement, and Bell's inequality. Because quantum computing resources are now publicly available, Jarrett Lancaster has written two papers showing how they can be used to teach quantum mechanics. Written with Brysen Allen (p. 98), a first paper shows how students can use freely available quantum hardware to simulate the dynamics of spin systems. Written with Nicholas Palladino, a second paper explores a question that regularly arises in introductory courses on quantum mechanics (p. 110): is it inherent to the theory that its fundamental quantities are complex numbers? Interestingly, they not only theorize about this question, but also show how working quantum computers can be used to test their statements.
We are proud to share this first installment of the special collection with our readers, and we hope that these papers will be the start of a year of celebrating and learning about quantum mechanics.