We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Offering a detailed account of the key concepts and mathematical apparatus of quantum mechanics, this textbook is an ideal companion to both undergraduate and graduate courses. The formal and practical aspects of the subject are explained clearly alongside examples of modern applications, providing students with the tools required to thoroughly understand the theory and apply it. The authors provide an intuitive conceptual framework that is grounded in a coherent physical explanation of quantum phenomena, established over decades of teaching and research in quantum mechanics and its foundations. The book's educational value is enhanced by the inclusion of examples and exercises, with solutions available to instructors, and an extensive bibliography is provided. Notes throughout the text provide fascinating context on the tumultuous history of quantum mechanics, the people that developed it, and the questions that still remain at its centre. This title is also available as Open Access on Cambridge Core.
The 'arrow of time,' a concept first introduced by Sir Arthur Eddington, reflects the one-way flow of time and its association with various physical asymmetries in thermodynamics, cosmology, quantum mechanics, field theories, and beyond. Yet, the foundations of the arrow of time continues to challenge physicists and philosophers, having profound implications across multiple theories and disciplines.This volume compiles insights from the international colloquium 'The Arrow of Time: From Local Systems to the Whole Univers' held in Buenos Aires in 2023. It explores diverse perspectives on the arrow of time in thermodynamics, quantum mechanics and cosmology, its relation to counterfactual reasoning, free will and the growing-block universe, the interplay between consciousness and time, and the implications of time-reversal invariance. Collectively, these contributions provide a rigorous and comprehensive analysis of the enduring enigma of time's unidirectional nature.
This book describes the development of our understanding of the strong interactions in particle physics, through its competing ideas and personalities, its false starts, blind alleys, and moments of glory – culminating with the author's discovery of quarks, real particles living in a deeper layer of reality. How were quarks discovered, what did physicists think they were, and what did they turn out to be? These questions are answered through a collection of personal remembrances. The focus is on the reality of quarks, and why that reality made them so difficult to accept. How Feynman and Gell-Mann practiced physics, with their contrasting styles and motivations, presented different obstacles to accepting this reality. And how was the author, as a graduate student, able to imagine their existence, and act on it? Science buffs, students, and experts alike will find much here to pique their interest and learn about quarks along the way.
Capturing the stories of sixteen women who made significant contributions to the development of quantum physics, this anthology highlights how, from the very beginning, women played a notable role in shaping one of the most fascinating and profound scientific fields of our time. Rigorously researched and written by historians, scientists, and philosophers of science, the findings in this interdisciplinary book transform traditional physics historiography. Entirely new sources are included alongside established sources that are examined from a fresh perspective. These concise biographies serve as a valuable counterweight to the prevailing narrative of male genius, and demonstrate that in the history of quantum physics, women of all backgrounds have been essential contributors all along. Accessible and engaging, this book is relevant for a wide audience including historians, scientists and science educators, gender theorists and sociologists.
Elizabeth Monroe, married Boggs (1913−1996), trained as a mathematician at Bryn Mawr, as a mathematical chemist at Cambridge, and as a theoretical chemist at Cornell, before joining the Manhattan Project at the Explosives Research Laboratory. Although her contributions to the fields of computational quantum chemistry, statistical mechanics, and explosives had lasting legacies, her scientific career nevertheless ended with World War II. The birth of her son, who suffered from severe developmental disabilities, prevented her from ever rejoining the research workforce. She pivoted instead to a remarkable life of public advocacy for people with disability, building on her scientific training to move research and policy forward. This chapters retraces how Monroe Boggs went from an early quantum chemistry enthusiast to a key figure of the disability rights movement.
In 1896, Edward Charles Pickering, Director of the Harvard College Observatory (HCO), reported in a trio of publications on the observation of “peculiar spectra” of the southern star ζ Puppis, which he attributed to an “element not yet found in other stars or on earth.” Supported by laboratory spectra obtained by Alfred Fowler, Niels Bohr showed in 1913 that this “element” was ionized helium. Its spectrum has become known as the Pickering series, even though Pickering credited Williamina Fleming (1857−1911), one of HCO’s “computers” and the future curator of the Astronomical Photographic Glass Plate Collection, for the discovery. The series of spectral lines associated with Pickering’s name played a unique role on the path to quantum mechanics,serving as a proving ground for Bohr’s model of the atom. Our examination of the discovery of the Pickering series relied on the records held at the Center for Astrophysics | Harvard & Smithsonian, especially the notebooks and diaries of Fleming, and on the center’s glass plate collection. Glimpses of the “peculiar sociology” of a research institution, half of whose staff were women employed on grossly unequal terms with men, are also given.
This chapter examines the contributions to quantum physics made by Lídia Salgueiro (1917–2009) and a team of women researchers at the Laboratory of Physics of the University of Lisbon. Between 1929 and 1947, the Lisbon laboratory rose to prominence as a successful research school in atomic and nuclear physics. The 1947 political purge by the dictatorial regime of the Estado Novo, however, led to a drastic reorganization, including the ousting of one of its leaders, Manuel Valadares. The right-wing physicist Julio Palacios was then appointed director. We here analyze how these institutional changes impacted Salgueiro’s agency. While Palacios opted for a new research agenda on electrochemistry, Salgueiro and women researchers gathered around her took responsibility for continuing research along the lines previously set up by Valadares. This group of women successfully extended their research into quantum physics to the study of radiation emitted at the atomic and nuclear levels, with a particular emphasis on X-ray spectroscopy. They asserted themselves as a relevant group within the Portuguese emerging research community in the field, participating in the many avenues asserting experimental atomic and nuclear physics on a global scale.
Spanish physicist Maria Lluïsa Canut (1924–2005) specialized in the application of X-ray diffraction to the determination of molecular crystal structures, a field at the intersection of crystallography and quantum mechanics. She completed her PhD at the University of Barcelona under the supervision of José Luís Amorós (1920–2001). After becoming a couple, the two developed joint research projects. In the 1960s, they moved to Southern Illinois University, where she notably built computing programs to analyze molecular structures from X-ray diffraction patterns. In parallel, Canut became involved in the struggle for pay parity at the university. This participation in the US second feminist wave sparked her interest in science policy. After the couple moved back to Madrid in the 1970s, Amorós continued with crystallographic research, whereas Canut became involved in American–Spanish scientific cooperation and computing systems applied to university libraries. This chapter analyzes Canut’s scientific contributions against the backdrop of her gender and across the changing contexts of her career, including the role played by scientific couples in the research enterprise.
In 1925, as matrix mechanics was taking shape, Lucy Mensing (1901−1995), who earned her PhD with Lenz and Pauli in Hamburg, came to Göttingen as a postdoc. She was the first to apply matrix mechanics to diatomic molecules, using the new rules for the quantization of angular momentum. As a byproduct, she showed that orbital angular momentum can only take integer values. Impressed by this contribution, Pauli invited her to collaborate on the susceptibility of gases. She then went to Tübingen, where many of the spectroscopic data were obtained that drove the transition from the old to the new quantum theory. It is hard to imagine better places to be in those years for young quantum physicists trying to make a name for themselves. This chapter describes these promising early stages of Mensing’s career and asks why she gave it up three years in. We argue that it was not getting married and having children that forced Lucy Mensing, now Lucy Schütz, out of physics, but the other way around. Frustration about her own research in Tübingen and about the prevailing male-dominated climate in physics led her to choose family over career.
The first four women to obtain a PhD in physics at Leiden University all graduated with Nobel laureate Hendrik Lorentz, among them Hendrika Johanna (Jo) van Leeuwen (1887−1974). She and her younger sister Cornelia (Nel) van Leeuwen finished their undergraduate studies in physics in Leiden in the early twentieth century. Whereas the younger sister left physics in 1917 after a relatively short period as a graduate student, Jo van Leeuwen went on to earn a PhD in 1919. Her thesis elucidates that magnetism is exclusively a quantum phenomenon – a result that was independently also obtained by Niels Bohr and that is now commonly known as the Bohr–van Leeuwen theorem. From 1920 onwards Van Leeuwen worked at the Technische Hoogeschool in Delft (now Delft University of Technology). Initially serving as an assistant, she was appointed as a reader in theoretical and applied physics in 1947, becoming the first female reader in Delft. This chapter outlines the foray into physics by the two sisters, focusing specifically on Jo van Leeuwen, detailing her work and early contributions to the quantum theory of magnetism.
Chien-Shiung Wu (1912–1997) is often referred to as “the Chinese Marie Curie” even though she conducted most of her research in the US. She is best known for her discovery of the non-conservation of parity for weakly interacting particles – a finding for which she is widely regarded as having been passed over for the 1957 Nobel Prize in Physics. Seven years earlier, though, in a one-page letter to Physical Review, Wu and her graduate student also quietly reported what has come to be understood as the first conclusive evidence of entangled photons. Twenty years later, as quantum foundations research emerged from shadow, Wu revisited her 1949 experiment with a more refined approach. Wu shared the new results with Stuart Freedman, a collaborator of John Clauser. Clauser et al. would rigorously critique Wu’s experiments through at least 1978. In 2022, the Nobel Committee honored Clauser, Alain Aspect, and Anton Zeilinger, each of whom had produced increasingly convincing proof of entanglement beginning in the 1970s. Wu’s foundational work from almost seventy years earlier, however, was not mentioned. This chapter aims to help bring Wu’s entangled photons back into the light.
Ana María Cetto Kramis (born 1946) studied physics at Universidad Nacional Autónoma de México and biophysics at Harvard University. As a faculty member back in Mexico, she spent over half a century delving into the fundamentals of quantum physics, with a singular focus on its stochastic interpretation. In addition to her theoretical work, she founded Latindex and has become a key figure in the open access movement. She has also had a long and influential contribution to international scientific cooperation. Her professional and personal journeys culminate with the dynamization of the International Year of Quantum Science and Technologies 2025, aiming to shed light on her understanding of quantum science and of science as a whole. This chapter is mostly based on an oral history, which is here also revisited as a historiographical methodology from its early use at the origins of the history of quantum physics.
In recent years, Grete Hermann (1901–1984) has been rediscovered as a principal figure in the history and philosophy of quantum physics. In particular, her criticism of Johann von Neumann’s so-called “no hidden variables” proof is a focal point of interest. Did she really find a mistake in this proof? We argue that the whole debate is misleading. It fits too well with the image of a forgotten woman who disproved a result of a mathematical genius, but it is neither historically nor systematically justified. Despite Hermann’s challenging thoughts on quantum physics, her impressive and important achievements were in ethics and politics. We offer a new and broader reading of Hermann’s interpretation of quantum physics and try to build a bridge between her works on quantum physics and ethics. In doing so, we focus on her interpretation of Heisenberg’s cut as a methaphorical device to argue against Leonard Nelson’s theory of free will and for freedom and responsibility as cornerstones of any democratic society.
Sonja Ashauer (1923–1948) trained as a physicist at the University of São Paulo in Brazil and obtained a PhD in theoretical and mathematical physics from the University of Cambridge, under the guidance of Paul Dirac. Acknowledged as the first Brazilian woman with a physics PhD, her life was brief: She passed away six months after defending her thesis. In her few contributions, she explored the non-physical consequences of classical equations for point electrons, reformulated by Dirac in the late 1930s to address divergence issues in quantum electrodynamics. This chapter traces Ashauer’s journey from São Paulo, where she collaborated with a small and enthusiastic group of young researchers around the Italian–Russian physicist Gleb Wataghin and focused on cosmic ray physics research, to Cambridge, where she found a more secluded research environment.
The chapter illustrates what it meant for Carolyn Beatrice Parker (1917–1966) to be a Black woman physicist in the US during the Jim Crow era. Her father, a physician, and her mother, a teacher, shepherded her into Fisk University, an historically Black college. As a physics major she studied infrared spectroscopy with the Black physicist Elmer Imes, graduating with a BS in 1938. She later attended the University of Michigan, obtaining an MA in physics in 1941. But like many Black women, she spent time before and after graduate school teaching in the K–12 system. In 1943, she became a research physicist at the Aircraft Radio Laboratory in Dayton, Ohio, where she stayed for four years. Although she co-authored a governmental report about her work on signal attenuation in coaxial cables, her name only appeared in the acknowledgments of the ensuing academic publications, thus partly obscuring her contributions. In 1947, Fisk University welcomed Parker on the faculty, but she soon after enrolled in a nuclear physics PhD program at the Massachusetts Institute of Technology. After dropping out, she worked as a laboratory technician until she grew too ill and died a short time later.
American physicist Freda Friedman Salzman (1927–1981) became an active feminist after her faculty position at the University of Massachusetts Boston was not renewed, under the university’s misogynistic anti-nepotism policy. Whereas her long-lasting struggle and eventual reappointment has already been expounded to some extent, her contributions to physics have not been given proper historical consideration. It is easier to learn about Friedman Salzman’s “weight of being a woman” – as she put it – than about her academic work. This chapter remedies that omission by shedding light on one of her key accomplishments. In 1956, Geoffrey Chew and Francis Low established the well-known Chew–Low model to put the understanding of nuclear interactions on a sounder theoretical basis. The model, however, leads to a daunting nonlinear integral equation. Friedman Salzman and her husband managed to solve the integral equation numerically. Stanley Mandelstam soon recognized the achievement of “Salzman and Salzman” (as he wrote) by naming their approach the “Chew–Low–Salzman method.”