Nuts and bolts of quantum mechanics
London, UK
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Energy is a purely abstract quantity, introduced into physics as a useful model with which we can short-cut complex calculations.
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📚 An excellent introduction to quantum mechanics for mathematicians with little prior exposure to physics 👍 #quantum #mathematics
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The fact is, all electrons are utterly identical, in a way that no two classical objects can ever be. It’s not just that we don’t know which electron is which; God doesn’t know which is which, because there is really no such thing as "this" electron, or "that" electron; all we can legitimately speak about is "an" electron.
— David J. Griffiths
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📽️ Hydrogen atom: 3d₀ orbital. Sampling the electron's position.
👉 piped.video/29yTOXsY4vM
#quantum #physics #chemistry
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📚 Mastering quantum mechanics requires a strong command of Lagrangian and Hamiltonian mechanics. Here is an exceptional resource for developing expertise in both of these areas.
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Everything in the future is a wave, everything in the past is a particle.
— Lawrence Bragg
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🆕📖 A fresh introduction to quantum mechanics, crafted to deliver the material in a clear and rigorous manner, tailored for first-year students in physics, mathematics, and engineering.
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📚 An undergraduate level textbook introducing the fundamentals of #quantum mechanics through spin systems 👍
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"... it is entirely possible that future generations will look back, from the vantage point of a more sophisticated theory, and wonder how we could have been so gullible."
— The closing sentence of Introduction to Quantum Mechanics by David J. Griffiths.
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📚 Two very valuable mathematics textbooks for aspiring quantum mechanics specialists
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📚 New on the Shelves
Contemporary Quantum Mechanics in Practice: Problems and Solutions
Lilia M. Woods & Pablo Rodríguez López
(Cambridge University Press, 2024)
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If you find your own comprehension slipping, from time to time [...], come back to the spin-1/2 system: It is the simplest and cleanest context for thinking through the conceptual paradoxes of quantum mechanics.
— David J. Griffiths
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Originally published in 1986, this book still holds relevance today. It appears that there has been limited progress in our understanding of the foundations of quantum mechanics over the past four decades.
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The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction.
— Sidney Coleman
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📚 A practical introduction designed for beginners with minimal prior knowledge of linear algebra or physics.
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A #quantum particle in a shrinking box. Probability density in position space and quasiprobability density (Wigner's function) in phase space.
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📚 A concise, modern introduction to quantum mechanics designed for readers with only a limited mathematical background. The book offers a historical overview, introduces fundamental concepts, explores Everett's many-worlds interpretation of quantum mechanics, and delves into the realms of quantum computing and communication.
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A #quantum particle bouncing between two parabolic mirrors. The initial state is a Gaussian wave packet centered at one of the foci. The cyan curve shows the center-of-mass trajectory.
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📚 A short, interesting book that introduces the basic concepts of quantum computing. Suitable for high-school and early undergraduate students.
Available for free download 👉 link.springer.com/content/pd…
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A lightning-speed introduction to #quantum physics for mathematicians. Covers nonrelativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics, and quantum field theory in just over 200 pages! 😯
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📚 An undergraduate-level textbook providing a modern, comprehensive introduction to quantum mechanics
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Introduction to Time-Dependent Quantum Mechanics with Python doi.org/10.1142/13434
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Our proposal would eradicate the collapse problem and the measurement problem. Even the existence of an "arrow of time" can perhaps be explained in a more elegant way than usual.
— Gerard 't Hooft
Open access 📖 link.springer.com/book/10.10…
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📚 This exceptionally clear and captivating book explores the conceptual meaning of quantum theory and scrutinises some of its key mathematical models.
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📚 A valuable collection of essays exploring the foundational and philosophical aspects of #quantum mechanics, including realism, ontology, and indeterminacy.
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Beginning with the big bang, the universe expands and cools. After eons of dynamic development it gives rise to observership. Acts of observer-participancy — via the mechanism of the delayed-choice experiment — in turn give tangible "reality" to the universe not only now but back to the beginning.
— John Archibald Wheeler
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📚 An overview of the collapse theories of quantum mechanics written by distinguished physicists and philosophers of physics.
doi.org/10.1017/978131699545…
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📚 The long-awaited second edition of the acclaimed elementary introduction to quantum optics doi.org/10.1017/978113915120…
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Quantum egg shaped billiard
piped.video/D3chcNT0iFQ
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Matter-wave diffraction: Barriers against slits
📽️ piped.video/2oDHC7uybdQ
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📚 This book offers a comprehensive and highly readable introduction to quantum mechanics. In addition to the standard topics, it features an outstanding chapter on quantum systems with time-dependent Hamiltonians, covering subjects such as the Landau-Zener transition, the Berry phase, a particle between moving walls, and a harmonic oscillator with a time-dependent frequency. The chapters on entanglement and measurement are also superb!
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📚 A brief, accessible, and unconventional introduction to both non-relativistic and relativistic quantum mechanics for undergraduates.
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If an apple is magnified to the size of the earth, then the atoms in the apple are approximately the size of the original apple.
— Richard Feynman
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The Historical and Physical Foundations of Quantum Mechanics
global.oup.com/academic/prod…
R. Golub and S. Lamoreaux
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Computer Scientists Prove That Heat Destroys Quantum Entanglement quantamagazine.org/computer-…
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📚 New on the Shelves
Old quantum theory and early quantum mechanics: A historical perspective commented for the inquiring reader
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Reflection of a #quantum particle from a mirror that is only three atomic layers thick. A small part of the probability density gets trapped by the mirror.
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The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts.
— Werner Heisenberg
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📖 The Theory of Quantum Information
Preprint available on the author's website: johnwatrous.com/the-theory-o…
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🌀 The Wigner function is a quasi-probability distribution in phase space that lets us analyze quantum states and observables with classical-like intuition. ✍️ Here’s a concise overview of its key features:
States: quantphys.com/post/wigner-s-…
Observables: quantphys.com/post/wigner-s-…
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📚 New on the Shelves
Quantum Mechanics through Problems
With Complete Solutions
Rocco Schiavilla
(Cambridge University Press, 2024)
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🌀 Quantum Harmonic Oscillator with a Time-Dependent Frequency
⚛️ The harmonic oscillator is a cornerstone model in physics -- simple, solvable, and deeply insightful. Even when its frequency changes with time (for example, in ion traps with dynamic electric fields), it can often be treated analytically. Here, we explore an exactly solvable case of the quantum harmonic oscillator with a time-dependent frequency 👉 quantphys.com/post/quantum-h…
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Quantum Machine Learning: A Hands-on Tutorial for Machine Learning Practitioners and Researchers arxiv.org/abs/2502.01146
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🎬 Quantum Particle Traversing a Reflectionless Potential
We are working on a short video that will provide a simple, understandable introduction to the concept of reflectionless potentials in quantum mechanics. Here's a sneak peek at a simulation featured in the video. It shows the probability density of a particle, represented by the red wave packet, moving through a Pöschl-Teller potential well. Additionally, the motion of the equivalent free particle is depicted by the blue wave packet for comparison. As evident, the particle smoothly traverses the potential well without experiencing any reflection.
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A #quantum billiard with a carefully chosen initial state. The billiard boundary is a Cassini oval:
en.wikipedia.org/wiki/Cassin…
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#quantum diffraction at a grating piped.video/rjnXEuO9-SE
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📚 New on the Shelves
The Conceptions of Reality in the Interpretations of Quantum Mechanics: A Journey from Aristotle’s Principles to Einstein’s Dreams of a Unified Theory
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On average, a #quantum particle launched from one focus of an elliptical cavity will (just) miss the other focus! 🎯❌
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📚 "[Intended for] students of physics, rather than of mathematics, whose mathematical equipment is limited, particularly at the beginning of their studies." — From the preface
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📚 "[N]one of the mysteries and paradoxes which plague the usual descriptions of quantum mechanics arise [in Bohmian mechanics]."
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📚 This book caters to both non-experts and experts — it has something valuable to offer to everyone!
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Quantum snowflake
Probability density of a #quantum particle placed in the center of the Koch snowflake billiard.
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✍️ The Madelung equations are a reformulation of the Schrödinger equation, one of the central principles of quantum mechanics, into a form that describes the flow of a (nonclassical) fluid. This brief note recaps the derivation of the Madelung equations: quantphys.com/post/madelung-…
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A self-contained textbook on nonrelativistic #quantum mechanics with ~600 fully solved examples and problems.
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✍️ A quantum particle under a uniform time-dependent force is one of the simplest exactly solvable cases of the Schrödinger equation with a time-dependent potential. Here's a brief overview: quantphys.com/post/quantum-p…
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A #quantum particle in a triangular billiard: the onset of pseudo-chaos
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❗️ Mathematica users can now write and execute quantum algorithms directly in the Mathematica environment, using QuEra's quantum computing resources: thequantuminsider.com/2023/0…
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A #quantum particle dropped into a U-shaped tube
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A Short Introduction to Quantum Computing for Physicists arxiv.org/abs/2306.09388
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📚 A modern, advanced undergraduate or graduate-level textbook on quantum mechanics. It effectively combines the presentation of a standard set of topics with a contemporary, in-depth introduction to quantum entanglement. Solid and invigorating!
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🌌 Quantum Tunneling
A glimpse into our Quantum Mechanics: Elementary Concepts course.
🔗 Full course here: quantphys.teachable.com/p/qu…
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📚 Quantum Mechanics: Elementary Concepts
A concise and rigorous course for beginners — completely free!
🎞️ Video lectures: piped.video/playlist?list=PL…
✍️ Solved exercises: quantphys.com/lessons/qm1
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📚 Mathematical foundations of quantum mechanics presented in great detail (~700 pp.) and with rigour. Readable, but calls for hard work! 😅
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Quantum Koch snowflake piped.video/usbsdlLaTBQ
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📖 Clear. Captivating. Illuminating. No prior knowledge of #quantum mechanics is required.
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🔥 Hot off the @arxiv
The unphysicality of Hilbert spaces arxiv.org/abs/2308.06669
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