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.

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.

I introduce quaternions by recounting the story of how Hamilton discovered them, but in far more detail than other authors give. This detail is necessary for the reader to understand why Hamilton wrote his quaternion equations in the way that he did. I describe the role of quaternions in rotation, show how to convert between them and matrices, and discuss their role in modern computer graphics. I describe a modern problem in detail whereby Hamilton’s original definition has been ‘hijacked’ in a way that has now produced much confusion. I end by describing how quaternions play a role in topology and quantum mechanics.

Chapter 2 serves as an introduction to the fundamental principles of quantum mechanics, focusing on closed systems. It begins with the historic Stern–Gerlach experiment, highlighting the discovery of quantum spin. The narrative then shifts to the mathematical framework of quantum mechanics, covering inner product spaces, Hilbert spaces, and linear operators. These concepts are crucial for understanding the behavior and manipulation of quantum states, the core of quantum information theory.

The chapter further explores the encoding of information in quantum states, emphasizing qubits, and discusses quantum measurements, revealing the probabilistic nature of quantum mechanics. Additionally, it addresses hidden variable models, offering insights into the deterministic versus probabilistic interpretations of quantum phenomena.

Unitary evolution and the Schrödinger equation are introduced as mechanisms for the time evolution of quantum states, showcasing the deterministic evolution in the absence of measurements. This section underscores the dynamic aspect of quantum systems, pivotal for advancements in quantum information theory.

Did Werner Heisenberg and Carl Friedrich von Weizsäcker compromise with the Nazis? The story begins with Albert Einstein, who became a target for conservative physicists like Philipp Lenard and Johannes Stark who could not follow Einstein’s physics, and the early Nazi Party that rejected Einstein as a Jew as well as his pacifism and internationalism. When Hitler came to power, Lenard and Stark gained great influence. Stark in particular tried to accumulate power but steadily lost influence through conflicts with other Nazis. When Stark’s nemesis, the theoretical physicist Arnold Sommerfeld, was going to retire and be succeeded by Werner Heisenberg, Stark launched a vicious attack on Heisenberg in the SS newspaper. Heisenberg appealed to SS Leader Heinrich Himmler and thanks to support from the aeronautical engineer Ludwig Prandtl was eventually rehabilitated by the SS. The established physics community then launched a counterattack against the “Aryan Physics” of Lenard and Stark, which included writing Einstein out of the history of relativity theory. This was arguably Heisenberg’s greatest compromise with Nazism.

This monograph is about the change in meaning and scope of human rights rules, principles, ideas and concepts, and the interrelationships and related actors, on moving from the physical domain into the online domain. The transposition into the digital reality can alter the meaning of well-established offline human rights to a wider or narrower extent; it can turn positivity into negativity and vice versa. The digital human rights realm has different layers of complexity in comparison with the offline realm.

This project uses the procedure of root-finding to resolve the eigenvalue problem of a rectangular quantum well. The procedure is applied to determine the first two to three energy levels of a simplified model of a hydrogen atom, represented by the rectangular quantum well. The project also explores the eigenvalue problem within various physics fields. While the project involves simple mathematical operations, it is rooted in complex physical concepts like quantum mechanics, often unfamiliar to first-year students. The fundamentals of quantum mechanics are introduced, providing enough understanding for successful project execution. The project initially focuses on the central object, the quantum state, and its probabilistic nature in quantum mechanics. The Schrödinger equation, an eigenvalue problem, is used to find state functions. This project explores eigenenergies and eigenfunctions within a rectangular finite quantum well, treating the well as a simplistic 1D model of the hydrogen atom.

Quantum field theory (QFT) provides us with one and almost only suitable language (or mathematical tool) for describing not only the motion and interaction of particles but also their “annihilation” and “creation” out of a field considered a priori in a sophisticated way, whose view seems to be suited for describing dislocations, as a particle or a string embedded within a crystalline ordered field. This chapter concisely overviews the method of QFT, emphasizing distinction from the quantum mechanics, conventionally used for a single and/or many particle problems, and its equivalence to the statistical mechanics. The alternative formalism based on Feynman path integral and its imaginary time representation are reviewed, as the foundation for our use in Chapter 10.

Basic concepts of quantum mechanics: Schroedinger equation; Dirac notation; the energy representation; expectation value; Hermite operators; coherent superposition of states and motion in the quantum world; perturbation Hamiltonian. Time-dependent perturbation theory: harmonic perturbation. Transition rate: Fermi’s golden rule. The density matrix; pure and mixed states. Temporal dependence of the density operator: von Neuman equation. Randomizing Hamiltonian. Longitudinal and transverse relaxation times. Density matrix and entropy.

In this chapter, we review basic concepts from quantum mechanics that will be required for the study of superconducting quantum circuits. We review the fundamental idea of energy quantization and how this can be formalized, using Dirac's ideas, to develop a quantum mechanical description that is consistent with the classical theory for a comparable object. We review the notions of quantum state, observable and projective and generalized measurements, particularizing some of these ideas to the simple case of a two-dimensional object or qubit.

Here we discuss the possible relation ofour generalconjecture on global attractors ofnonlinear Hamiltonian PDEs todynamicaltreatment of Bohr's postulates and of wave--particle duality, which are fundamental postulates of quantum mechanics, in the context of couplednonlinear Maxwell--SchrödingerandMaxwell--Dirac equations. The problem of adynamicaltreatment was the main inspiration for our theoryof global attractors ofnonlinear Hamiltonian PDEs.

The interest taken by Surrealists in alchemy has been well known since the late 1940s, but knowledge of their preoccupation with modern science is more recent. This chapter observes the Surrealist penchant for premodern, occultist epistemologies before focusing on their take up of modern physics in the early 1920s. The theory of relativity (1905 and 1915–16) and developments in quantum mechanics (1922–7) were then undergoing popularization. Apart from popular articles in newspapers/journals, this occurred partly through physicists’ own writings and partly through the philosophy of science. This chapter indicates the importance to Surrealism of the writings of the French philosopher of science, Gaston Bachelard. It also features a case study of the work of German physicist Pascual Jordan whose attempt to extend the findings of quantum mechanics to biology was known to Max Ernst and used by the Surrealists to justify the rejection of positivism. So modern physics became a means of retrospectively comprehending the Surrealists’ turn towards automatism and Ernst’s own natural history incursions. His response to Jordan’s writings offers an alternative way of reading his work.