General
Biographies
Classical Mechanics
- Classical Mechanics, Charles Taylor (2005). Easy to read, well explained, at the level of 2nd undergrad course in mechanics. Reputed to have the best explanation of the Lagrangian. Replete with well picked exercises. Requires a bit of calculus - derivatives, integrals, very basic PDEs. No differential geometry required.
- Mathematical Methods of Classical Mechanics, V.I. Arnold, 2nd ed (1989)
- Mechanics: Course of Theoretical Physics, Lev Landau, Evgenij M. Lifshitz (1976), review
- Introduction to Mechanics and Symmetry, J.E. Marsden, T.S.Ratiu, 2nd ed (2010)
Gravitation
- Gravitation, Misner, Thorne, Wheeler (1973). I have not read it, but it’s supposed to be ‘the’ reference on gravity as of the 1970s. And it’s supposed to have really clear physical interpretation of differential geometric concepts.
Statistical Mechanics
Ising Model
Quantum Mechanics
- Quantum Field Theory for the Gifted Amateur, T. Lancaster, S. J. Blundell (2014)
- A Mathematical Companion to Quantum Mechanics, S. Sternberg (2019)
- Physics from Symmetry, J. Schwichtenberg (2015)
- Quantum Mechanics in Simple Matrix Form, Thomas F. Jordan (1986). An exposition in the simplest operator form, starting from 2x2 matrices, and avoiding any discussion of eigenvalues, hermitian matrices, etc.
- Quantum Theory for Mathematicians, Brian C. Hall (2013), homepage, review
- A Modern Approach to Quantum Mechanics, John S. Townsend (2021)
- 101 Quantum Questions, Kenneth W. Ford (2011). For some reason, this is an easier read, perhaps because it speaks, at least in the earlier sections, of the experiments that resulted in the discoveries of various elementary particles and quantum effects. This makes it an ideal companion to the more mathematically inclined books.
- G.W. Mackey: Unitary Group Representations in Physics, Probability, and Number Theory (1978)
- L. Mangiarotti et al: Geometric and Algebraic Topological Methods in Quantum Mechanics (2005)
- L. Susskind: Copenhagen vs Everett, Teleportation, and ER=EPR (2016)
- Andy Matuschak and Michael Nielsen: Quantum computing for the very curious (2019)
Axiomatic Systems for Quantum Mechanics
Geometric Quantization
Geometric Mechanics
Lecture Notes
Courses
- Leonard Susskind: All Stanford physics lectures in order
- Classical Mechanics (Fall 2011)
- Lecture 1 Newton’s laws
- Lecture 2 Principle of least action. Lagrangian.
- Lecture 3. Proof of the principle of least action. Equivalence with Newton’s laws. Examples.
- Lecture 4. Lagrangian in polar coordinates. Continuous symmetries and the Noether Theorem. Conservation of energy. Hamiltonian.
- Lecture 5 Examples. Conservation of energy. Noether’s theorem.
- Lecture 6 Using Lagrangians to solve simple problems: Object sliding on inclined plane which slides on horizontal plane. Double pendulum. The Hamiltonian. Hamilton’s equations. Example: the harmonic oscillator.
- Lecture 7 The Hamiltonian as energy. Divergence. The Liouville theorem. Definition of Poisson bracket.
- Lecture 8 Poisson brackets \(\{F, G\}\). Poisson brackets in coordinates $q, p$. Derivation of \(\dot{F} = \{F, H\}\) for the Hamiltonian \(H\). Symmetries and conservation seen through the Poisson bracket - the Hamiltonian version of the Noether theorem. Angular momentum \(L_x = yp_z - zp_y\), \(L_y = zp_x - xp_z\), \(L_z = xp_y - yp_x\), its Poisson brackets with \(x, y, z\) and other angular momentum components \(L_x, L_y, L_z\). The gyroscope. Not mentioned: Poisson brackets also satisfy a Jacoby identity.
- Lecture 9 Gradient, curl, divergence. Divergence of curl is zero. Fields with zero divergence are curls. Curl of gradient is zero. Fields with zero curl are gradients. Electrostatic field \(\vec{E}\). Magnetic field \(\vec{B}\). Comparison of magnetic force with Coriolis force. Zero divergence of magnetic field. Vector potential \(\vec{A}\) defined so its curl is \(\vec{B}\). Non-uniqueness of \(\vec{A}\), up to gauge transformation \(\vec{A} + \vec{\nabla}f\). Origin of term gauge as historical glitch. Lorenz force \(\vec{F} = e (-\vec{\nabla}V + \frac{\vec{v}}{c} \times \vec{B})\). Lagrangian for Lorenz force \(\mathcal{L} = \frac{m}{2} \dot{x}^2 - eV + \frac{e}{c} \vec{A} \cdot \dot{x}\). Gauge invariance of the Lagrangian least action.
- Lecture 10 Lagrangian of a particle in a magnetic field. Gauge invariance. Mechanical vs. canonical momentum. The Hamiltonian. Motion of a charged particle in a uniform magnetic field. Non-existence in practice of magnetic monopoles. Theoretical construction of a magnetic monopole.
- Quantum Entanglement (2006)
- Lecture 1 Classical bits. States in classical Physics. Transformations. Reversibility. Computability of states and transformations. Vectors, matrices.
- Lecture 2: Electron spin. Complex vector spaces. Bra-kets. Quantum bit. Hermitian matrices as observables.
- Lecture 3 Pauli matrices. Spin. Probabilistic interpretation.
- Lecture 4 Probabilities between any two spin directions. There always exist a direction for which a vector is an eigenvector of measuring spin in that direction. Quantum entagled pair of electrons. How to create an entangled pair.
- General Relativity (Fall 2012), not yet watched
- Quantum Mechanics (Winter 2012), not yet watched
- Special Relativity and Electrodynamics (Spring 2012), not yet watched
- Cosmology (Winter 2013), not yet watched
- Statistical Mechanics (Spring 2013), Andrei’s notes
- Supplemental Courses, Archived Courses
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