Quantum Mechanics
The definitive, comprehensive worldwide university-level course on Quantum Mechanicsβfrom mathematical foundations through advanced topics in modern quantum theory.
Course Overview
This course provides a rigorous, comprehensive treatment of quantum mechanics at the university level. With over 450 pages of detailed content, it serves as both a complete textbook and a reference work for students and researchers.
π What You'll Learn
- β’ Mathematical foundations: Hilbert spaces & operators
- β’ Core postulates and physical interpretation
- β’ Solutions to fundamental quantum systems
- β’ Angular momentum and spin theory
- β’ Approximation methods for complex systems
- β’ Identical particles and quantum statistics
- β’ Scattering theory and S-matrix formalism
- β’ Advanced topics: path integrals, entanglement, quantum information
π― Prerequisites
- β’ Calculus (single & multivariable)
- β’ Linear algebra (vectors, matrices, eigenvalues)
- β’ Differential equations (ODE & PDE)
- β’ Classical mechanics basics
- β’ Complex analysis (helpful)
- β’ Basic electromagnetism (helpful)
450+ pages | 9 major parts | 55+ chapters | Hundreds of equations
πΊ Video Lectures
World-class lectures on quantum mechanics, foundations, and the quantum-gravity interface from leading physicists.
Slavoj Ε½iΕΎek & Sean Carroll: Quantum Physics, the Multiverse, and Time Travel
A general discussion between renowned physicists exploring the philosophical and physical implications of quantum mechanics, including many-worlds interpretation, quantum measurement, and the nature of time.
Roger Penrose: Why Quantum Theory Is Fundamentally Wrong
Nobel laureate Sir Roger Penrose challenges the standard interpretation of quantum mechanics, discussing measurement problems, wavefunction collapse, and his proposal for objective reduction linked to quantum gravity.
Roger Penrose: We Need to 'Gravitise' Quantum Mechanics, Not Quantise Gravity - Full Interview
Full interview with Roger Penrose discussing his radical perspective on the quantum-gravity problem. He argues that quantum mechanics needs modification at the Planck scale, rather than simply quantizing general relativity.
The Quantum Frontier with Brian Greene and John Preskill
Renowned Caltech physicist John Preskill joins Brian Greene for an in-depth discussion of quantum mechanics, focusing on where we are and where we're headed with quantum computing. This conversation explores the frontiers of quantum information theory, quantum algorithms, quantum error correction, and the race to achieve quantum supremacy.
Topics Covered:
- Foundations of quantum computing and quantum bits (qubits)
- Quantum algorithms: Shor's algorithm, Grover's algorithm
- Quantum error correction and fault tolerance
- Current state of quantum hardware and technology
- Future applications: cryptography, simulation, optimization
- The path toward practical quantum computers
John Preskill: Quantum Computing and the Entanglement Frontier
The quantum laws governing atoms and other tiny objects seem to defy common sense, and information encoded in quantum systems has weird properties that baffle our feeble human minds. John Preskill explains why he loves quantum entanglement, the elusive feature making quantum information fundamentally different from information in the macroscopic world. By exploiting quantum entanglement, quantum computers should be able to solve otherwise intractable problems, with far-reaching applications to cryptology, materials, and fundamental physical science.
Key Topics:
- Quantum entanglement and its role in quantum information
- Why quantum information differs from classical information
- How quantum computers exploit entanglement
- Applications to cryptography and materials science
- Implications for fundamental physics
- The entanglement frontier in quantum computing
John Preskill: Feynman's Dream - Simulating Nature with Quantum Machines
As part of the Distinguished Speakers series at the Qiskit Global Summer School, Professor John Preskill presents Feynman's Dream: Simulating Nature with Quantum Machines. In this talk, he explores the origins of quantum computing, beginning with Richard Feynman's seminal 1981 lecture that proposed using quantum systems to simulate quantum phenomena. Preskill reflects on key milestones over the decades, including contributions from Heisenberg and Dirac, and marks the centennial of quantum mechanics. With both historical perspective and forward-looking insight, he shows how foundational ideas planted the seeds for the vibrant and fast-moving field of quantum information science today.
Historical Journey:
- Richard Feynman's 1981 seminal lecture on quantum simulation
- Origins of quantum mechanics: Heisenberg and Dirac
- Historical milestones in quantum information science
- From foundational ideas to modern quantum computing
- The centennial of quantum mechanics
- Future prospects for quantum simulation and computing
John Preskill: From the Early Universe to the Future of Quantum Computing
As Director of the Caltech Institute for Quantum Information and Matter, John Preskill leads one of the most vibrant programs exploring quantum information and quantum computation. In this fascinating discussion, he explores this rapidly evolving field, about which so much is written in the popular press, and which may impact all of our lives in the 21st century. The conversation separates wheat from chaff, discussing the future of the field, its current state, and challenges and opportunities. Preskill also reflects on his own scientific career, the physics areas that have excited him, and what helped drive him to become a physicist in the first place. It is both entertaining and enlightening.
Discussion Topics:
- Current state of quantum computing technology
- Future prospects and realistic timelines for quantum computers
- Separating hype from reality in quantum computing
- Preskill's scientific career and journey to quantum physics
- Challenges and opportunities in quantum information science
- Potential impacts of quantum computing on 21st century technology
John Preskill: Holographic Quantum Codes
Two of the most amazing ideas in physics are the holographic principle and quantum error correction. The holographic principle asserts that all the information contained in a region of space is encoded on the boundary of the region, albeit in a highly scrambled form. Quantum error correction is the foundation of our hope that large-scale quantum computers can be operated to solve hard problems. Preskill argues that these two ideas are closely related, and describes quantum codes which realize the holographic principle. These codes provide simplified models of quantum spacetime, opening new directions in the study of quantum gravity, though many questions remain.
Key Concepts:
- The holographic principle in quantum gravity
- Quantum error correction and fault-tolerant computing
- Connection between holography and quantum codes
- Holographic quantum codes as models of spacetime
- Implications for quantum gravity research
- Open questions at the intersection of quantum information and gravity
Course Structure
Part I: Mathematical Foundations
Hilbert spaces, linear operators, eigenvalues, Dirac notation, tensor products, group theory, and representation theory.
Part II: Foundations of Quantum Mechanics
Historical development, postulates of QM, wave functions, measurement theory, uncertainty principle, and interpretations.
Part III: One-Dimensional Systems
Free particle, square wells, harmonic oscillator, delta function potentials, scattering, tunneling, and WKB approximation.
Part IV: Three-Dimensional Systems
3D SchrΓΆdinger equation, central potentials, angular momentum, spherical harmonics, hydrogen atom, and 3D scattering.
Part V: Spin & Angular Momentum
Spin-1/2, Pauli matrices, general angular momentum, addition of angular momenta, Clebsch-Gordan coefficients, SO(3) & SU(2).
Part VI: Approximation Methods
Time-independent and time-dependent perturbation theory, fine structure, Fermi's golden rule, variational and adiabatic methods.
Part VII: Identical Particles
Symmetrization postulate, fermions and bosons, Pauli exclusion, multi-electron atoms, periodic table, and exchange interaction.
Part VIII: Scattering Theory
Cross sections, Born approximation, partial wave analysis, phase shifts, resonances, and S-matrix theory.
Part IX: Advanced Topics
Path integrals, density matrix, entanglement, Bell's inequalities, decoherence, quantum information, and relativistic QM.
Why This Course?
π Worldwide Standard
Designed as the worldwide reference for university quantum mechanics courses, with rigor matching top physics departments.
π Comprehensive
450+ pages cover everything from mathematical foundations to cutting-edge topics, leaving no gaps in understanding.
β¨ Clear Exposition
Every concept explained from the ground up with detailed derivations, physical intuition, and worked examples.
Start with Mathematical Foundations