Physics Self-Study

Between 2023 and 2024, I was not enrolled in a physics program.

For about one year, I self-studied physics using established textbooks.

This page contains my solutions to textbook exercises, signed and dated.

Later (Sep 2024), I enrolled in the MSc Physics at Imperial College London.

Classical Mechanics

H. Goldstein, C. Poole & J. Safko, Classical Mechanics, 3rd ed. (42 worked solutions)

  • 1. Survey of the elementary principles
    • Exercise 1.1: PDF.
    • Exercise 1.2: PDF.
    • Exercise 1.3: PDF.
    • Exercise 1.8: PDF.
    • Exercise 1.9: PDF.
    • Exercise 1.12: PDF.
    • Exercise 1.14: PDF.
    • Exercise 1.15a: PDF.
    • Exercise 1.19: PDF.
    • Exercise 1.21: PDF.
  • 2. Variational principles and Lagranges equations
    • Exercise 2.3: PDF.
    • Exercise 2.4: PDF.
    • Exercise 2.5notSure: PDF.
    • Exercise 2.10: PDF.
    • Exercise 2.12: PDF.
    • Exercise 2.13: PDF.
    • Exercise 2.14: PDF.
    • Exercise 2.20: PDF.
  • 3. The central force problem
    • Exercise 3.10: PDF.
    • Exercise 3.11: PDF.
    • Exercise 3.19a: PDF.
  • 4. The kinematics of rigid body motion
    • Exercise 4.2: PDF.
    • Exercise 4.10: PDF.
  • 6. Oscillations
    • Exercise 6.1: PDF.
    • Exercise 6.2: PDF.
    • Exercise 6.3: PDF.
    • Exercise 6.12: PDF.
    • Exercise 6.13: PDF.
  • 7. The classical mechanics of the special theory of relativity
    • Exercise 7.6: PDF.
    • Exercise 7.13: PDF.
    • Exercise 7.19: PDF.
    • Exercise 7.20: PDF.
  • 8. The Hamiltonian equations of motion
    • Exercise 8.1: PDF.
    • Exercise 8.2: PDF.
    • Exercise 8.7: PDF.
    • Exercise 8.12: PDF.
  • 9. Canonical transformations
    • Exercise 9.2: PDF.
    • Exercise 9.4: PDF.
    • Exercise 9.5: PDF.
    • Exercise 9.17: PDF.
    • Exercise 9.21: PDF.
    • Exercise 9.24: PDF.

Classical Electrodynamics

D. Griffiths, Intro. to Electrodynamics, 4th ed. (9 worked solutions)

  • 3. Special techniques
    • Exercise 3.29v: PDF.
    • Exercise 3.30v: PDF.
    • Exercise 3.31v: PDF.
    • Exercise 3.32v: PDF.
  • 4. Electric fields in matter
    • Exercise 4.5v: PDF.
    • Exercise 4.10: PDF.
    • Exercise 4.19: PDF.
  • 9. Electromagnetic waves
    • Exercise 9.2: PDF.
    • Exercise 9.8abc: PDF.

J. Jackson, Classical Electrodynamics, 3rd ed. (38 worked solutions)

  • 1. Introduction to electrostatics
    • Exercise 1.1a: PDF.
    • Exercise 1.3: PDF.
  • 2. Boundary-value problems in electrostatics I
    • Exercise 2.1a: PDF.
    • Exercise 2.2: PDF.
    • Exercise 2.4ab: PDF.
    • Exercise 2.5a: PDF.
    • Exercise 2.8abc: PDF.
    • Exercise 2.11ab: PDF.
    • Exercise 2.14a: PDF.
    • Exercise 2.23a: PDF.
    • Exercise 2.26: PDF.
    • Exercise 2.extra: PDF.
  • 3. Boundary-value problems in electrostatics II
    • Exercise 3.1: PDF.
    • Exercise 3.2a: PDF.
    • Exercise 3.4b: PDF.
    • Exercise 3.6: PDF.
    • Exercise 3.7a: PDF.
    • Exercise 3.9: PDF.
    • Exercise 3.10a: PDF.
  • 4. Multiples electrostatics of macroscopic media dielectrics
    • Exercise 4.1ab: PDF.
    • Exercise 4.5ab: PDF.
    • Exercise 4.6ab: PDF.
    • Exercise 4.7a: PDF.
    • Exercise 4.8a: PDF.
    • Exercise 4.12scratch: PDF.
  • 5. Magnetostatics Faradays law quasi-static fields
    • Exercise 5.3: PDF.
    • Exercise 5.5ascratch: PDF.
    • Exercise 5.7ac: PDF.
    • Exercise 5.19a: PDF.
    • Exercise 5.21: PDF.
  • 6. Maxwell equations macroscopic electromagnetism conservation laws
    • Exercise 6.2a: PDF.
    • Exercise 6.4a: PDF.
    • Exercise 6.4bscratch: PDF.
    • Exercise 6.4cscratch: PDF.
    • Exercise 6.5a: PDF.
    • Exercise 6.11a: PDF.
  • 7. Plane electromagnetic waves and wave propagation
    • Exercise 7.1: PDF.
  • 11. Special theory of relativity
    • Exercise 11.3: PDF.

Quantum Field Theory and Particle Physics

D. Griffiths, Introduction to Elementary Particles, 2nd ed. (29 worked solutions)

  • 2. Elementary particle dynamics
    • Exercise 2.1: PDF.
    • Exercise 2.2: PDF.
    • Exercise 2.3: PDF.
  • 4. Symmetries
    • Exercise 4.15: PDF.
    • Exercise 4.17: PDF.
    • Exercise 4.21: PDF.
    • Exercise 4.23: PDF.
    • Exercise 4.24: PDF.
    • Exercise 4.27: PDF.
    • Exercise 4.28: PDF.
  • 5. Bound states (from 1st ed)
    • Exercise 5.1: PDF.
    • Exercise 5.3: PDF.
    • Exercise 5.10: PDF.
    • Exercise 5.11: PDF.
  • 6. The Feynman calculus
    • Exercise 6.7: PDF.
    • Exercise 6.8: PDF.
  • 7. Quantum Electrodynamics
    • Exercise 7.9: PDF.
    • Exercise 7.10: PDF.
    • Exercise 7.27: PDF.
    • Exercise 7.28: PDF.
    • Exercise 7.30: PDF.
    • Exercise 7.32: PDF.
    • Exercise 7.37progress: PDF.
    • Exercise 7.42progress: PDF.
  • 8. Electrodynamics and chromodynamics of quarks
    • Exercise 8.1: PDF.
    • Exercise 8.2: PDF.
    • Exercise 8.13: PDF.
    • Exercise 8.14: PDF.
    • Exercise 8.15: PDF.

M. Schwartz, Quantum Field Theory and the Standard Model. (40 worked solutions)

  • 2. Lorentz invariance and second quantization
    • Exercise 2.1: PDF.
    • Exercise 2.2: PDF.
    • Exercise 2.6: PDF.
  • 3. Classical field theory
    • Exercise 3.1a: PDF.
    • Exercise 3.5: PDF.
    • Exercise 3.6acd: PDF.
  • 5. Cross sections and decay rates
    • Exercise 5.1: PDF.
    • Exercise 5.2: PDF.
    • Exercise 5.3: PDF.
  • 6. The S-matrix and time-ordered products
    • Exercise 6.1: PDF.
    • Exercise 6.2: PDF.
    • Exercise notes on feynman propagator: PDF.
  • 7. Feynman rules
    • Exercise 7.1: PDF.
    • Exercise 7.2: PDF.
    • Exercise 7.3: PDF.
    • Exercise 7.4: PDF.
    • Exercise 7.6inprogress: PDF.
    • Exercise 7.7: PDF.
    • Exercise check of eq 7-12: PDF.
  • 8. Spin-1 and gauge invariance
    • Exercise 8.1: PDF.
    • Exercise 8.2: PDF.
    • Exercise 8.3: PDF.
    • Exercise 8.4: PDF.
    • Exercise 8.5ab: PDF.
    • Exercise 8.6ab: PDF.
  • 9. Scalar quantum electrodynamics
    • Exercise 9.1a: PDF.
  • 10. Spinors
    • Exercise 10.1ab: PDF.
    • Exercise 10.2abd: PDF.
    • Exercise 10.4: PDF.
  • 11. Spinor solutions and CPT
    • Exercise 11.1abcd: PDF.
    • Exercise 11.2: PDF.
    • Exercise 11.5: PDF.
    • Exercise 11.6ab: PDF.
  • 13. Quantum electrodynamics
    • Exercise 13.1inprogress: PDF.
  • 15. The Casimir effect
    • Exercise 15.2: PDF.
  • 16. Vacuum polarization
    • Exercise 16.1: PDF.
    • Exercise 16.2inprogress: PDF.
  • 25. Yang-Mills theory
    • Exercise 25.1: PDF.
    • Exercise 25.2: PDF.
    • Exercise 25.4inprogress: PDF.

S. Weinberg, The Quantum Theory of Fields, vol. I & II. (4 worked solutions)

  • 2. Relativistic quantum mechanics
    • Exercise 2.1: PDF.
    • Exercise 2.2: PDF.
    • Exercise 2.5: PDF.
  • 3. Scattering theory
    • Exercise 3.1: PDF.

General Relativity

B. Schutz, A First Course in General Relativity, 3rd ed. (33 worked solutions)

  • 4. Perfect fluids in special relativity
    • Exercise 4.4: PDF.
    • Exercise 4.5: PDF.
    • Exercise 4.6: PDF.
    • Exercise 4.7: PDF.
  • 5. Preface to curvature
    • Exercise 5.7: PDF.
    • Exercise 5.12: PDF.
  • 6. Curved manifolds
    • Exercise 6.7a: PDF.
    • Exercise 6.11: PDF.
    • Exercise 6.21: PDF.
    • Exercise 6.28: PDF.
    • Exercise 6.29: PDF.
    • Exercise 6.30: PDF.
    • Exercise 6.31: PDF.
    • Exercise 6.32: PDF.
    • Exercise 6.33: PDF.
    • Exercise 6.35: PDF.
    • Exercise 6.38: PDF.
    • Exercise 6.39: PDF.
  • 7. Physics in a curved spacetime
    • Exercise 7.1: PDF.
    • Exercise 7.2: PDF.
    • Exercise 7.3: PDF.
    • Exercise 7.4: PDF.
    • Exercise 7.6: PDF.
    • Exercise 7.7: PDF.
  • 8. The Einstein field equations
    • Exercise 8.1: PDF.
    • Exercise 8.2: PDF.
    • Exercise 8.4: PDF.
    • Exercise 8.5: PDF.
    • Exercise 8.6: PDF.
    • Exercise 8.7: PDF.
    • Exercise 8.8a: PDF.
    • Exercise 8.10: PDF.
    • Exercise 8.12: PDF.

G. ‘t Hooft, Introduction to General Relativity (lecture notes). (11 worked solutions)

  • 4. Curved coordinates
    • Exercise 4.1: PDF.
  • 5. The affine connection Riemann curvature
    • Exercise 5.1: PDF.
    • Exercise 5.2: PDF.
  • 8. The action principle
    • Exercise 8.1: PDF.
  • 10. Electromagnetism
    • Exercise 10.1: PDF.
    • Exercise 10.2: PDF.
  • 11. The Schwarzschild solution
    • Exercise 11.1: PDF.
  • 12. Mercury and light rays in the Schwarzschild metric
    • Exercise 12.1: PDF.
    • Exercise 12.2: PDF.
  • 13. Generalizations of the Schwarzschild metric
    • Exercise 13.2: PDF.
  • 14. The Robertson-Walker metric
    • Exercise 14.1: PDF.

P. Townsend, Black Holes (lecture notes), arXiv:9707012[gr-qc]. (9 worked solutions)

  • 2. Schwarzschild black hole
    • Exercise 2.18: PDF.
    • Exercise 2.20: PDF.
    • Exercise 2.24: PDF.
    • Exercise 2.41: PDF.
    • Exercise 2.60: PDF.
    • Exercise 2.90: PDF.
    • Exercise 2.118: PDF.
  • A2. Example Sheet 2
    • Exercise A2.1: PDF.
    • Exercise A2.2: PDF.

String Theory

J. Polchinski, String Theory, vol. I & II. (24 worked solutions)

  • 1. A first look at strings
    • Exercise 1.1a: PDF.
    • Exercise 1.1b: PDF.
    • Exercise 1.2: PDF.
    • Exercise 1.3: PDF.
    • Exercise 1.4a: PDF.
  • 2. Conformal field theory
    • Exercise 2.1a: PDF.
    • Exercise 2.2: PDF.
    • Exercise 2.3a: PDF.
    • Exercise 2.4: PDF.
    • Exercise 2.5: PDF.
    • Exercise 2.6: PDF.
    • Exercise 2.7a: PDF.
    • Exercise 2.7b: PDF.
    • Exercise 2.8: PDF.
    • Exercise 2.12a: PDF.
    • Exercise polchinski_2.9: PDF.
  • 3. The Polyakov path integral
    • Exercise 3.1a: PDF.
    • Exercise 3.2ab: PDF.
    • Exercise 3.3a: PDF.
    • Exercise 3.4: PDF.
    • Exercise 3.6: PDF.
  • 10. Type I and type II superstrings
    • Exercise 10.1a: PDF.
    • Exercise 10.2: PDF.
  • A. A short course on path integrals
    • Exercise A.1: PDF.

G. ‘t Hooft, Introduction to String Theory (lecture notes). (2 worked solutions)

  • 2. The classical string
    • Exercise 2.1: PDF.
  • 3. Open and closed strings
    • Exercise 3.1: PDF.

Thermal & Statistical Physics

H. Callen, Thermodynamics and an Intro. to Thermostatistics, 2nd ed. (14 worked solutions)

  • 2. The conditions of equilibrium
    • Exercise 2.2-1: PDF.
    • Exercise 2.2-4: PDF.
    • Exercise 2.3-2: PDF.
  • 3. Some formal relationships and sample systems
    • Exercise 3.2-1: PDF.
    • Exercise 3.3-1notSure: PDF.
    • Exercise 3.3-2: PDF.
    • Exercise 3.4-3: PDF.
    • Exercise 3.5-2: PDF.
    • Exercise 3.6-1: PDF.
    • Exercise 3.6-2: PDF.
  • 4. Reversible processes and the maximum work theorem
    • Exercise 4.2-1: PDF.
    • Exercise 4.2-3: PDF.
    • Exercise 4.4-1: PDF.
    • Exercise 4.4-2anotSure: PDF.

E. Fermi, Thermodynamics. (2 worked solutions)

  • 4. Entropy
    • Exercise 4.1: PDF.
    • Exercise 4.2: PDF.

M. Glazer & J. Wark, Statistical Mechanics: A Survival Guide. (13 worked solutions)

  • 1. Back to basics
    • Exercise 1.3: PDF.
  • 2. The statistics of distinguishable particles
    • Exercise 2.4: PDF.
    • Exercise 2.7: PDF.
  • 3. Paramagnet and oscillators
    • Exercise 3.2: PDF.
    • Exercise 3.3: PDF.
  • 4. Indistinguishable particles and monatomic ideal gases
    • Exercise 4.1: PDF.
  • 5. Diatomic ideal gases
    • Exercise 5.1: PDF.
  • 7. Electrons in metals
    • Exercise 7.1: PDF.
    • Exercise 7.2: PDF.
    • Exercise 7.5: PDF.
  • 8. Photons and phonons
    • Exercise 8.1: PDF.
    • Exercise 8.4: PDF.
    • Exercise 8.5: PDF.

C. Kittel & H. Kroemer, Thermal Physics, 2nd ed. (20 worked solutions)

  • 2. Entropy and temperature
    • Exercise 2.1: PDF.
    • Exercise 2.2: PDF.
    • Exercise 2.3: PDF.
    • Exercise 2.4: PDF.
  • 3. Boltzmann distribution and Helmholtz free energy
    • Exercise 3.1: PDF.
    • Exercise 3.3: PDF.
    • Exercise 3.4: PDF.
    • Exercise 3.5: PDF.
    • Exercise 3.8: PDF.
  • 4. Thermal radiation and Planck distribution
    • Exercise 4.1: PDF.
    • Exercise 4.2: PDF.
    • Exercise 4.5: PDF.
  • 5. Chemical potential and Gibbs distribution
    • Exercise 5.1: PDF.
    • Exercise 5.4: PDF.
    • Exercise 5.6: PDF.
  • 6. Ideal gas
    • Exercise 6.1: PDF.
    • Exercise 6.2: PDF.
  • 7. Fermi and Bose gases
    • Exercise 7.2: PDF.
    • Exercise 7.3: PDF.
  • 8. Heat and work
    • Exercise 8.1x: PDF.

R.K. Pathria & P. Beale, Statistical Mechanics, 4th ed. (5 worked solutions)

  • 1. The statistical basis of thermodynamics
    • Exercise 1.2: PDF.
    • Exercise 1.7: PDF.
    • Exercise 1.8: PDF.
  • 2. Elements of ensemble theory
    • Exercise 2.1: PDF.
    • Exercise 2.4: PDF.

Solid State Physics

C. Kittel, Introduction to Solid State Physics, 8th ed. (21 worked solutions)

  • 1. Crystal structure
    • Exercise 1.1: PDF.
    • Exercise 1.2correction: PDF.
    • Exercise 1.2x: PDF.
    • Exercise 1.3: PDF.
  • 2. Wave diffraction and the reciprocal lattice
    • Exercise 2.1a correction: PDF.
    • Exercise 2.1x: PDF.
    • Exercise 2.2ab: PDF.
    • Exercise 2.3: PDF.
    • Exercise 2.4: PDF.
  • 3. Crystal binding and elastic constants
    • Exercise 3.1: PDF.
    • Exercise 3.2: PDF.
    • Exercise 3.3: PDF.
    • Exercise 3.5: PDF.
    • Exercise 3.extra1: PDF.
  • 4. Phonons I crystal vibrations
    • Exercise 4.1: PDF.
    • Exercise 4.4: PDF.
  • 6. Free electron fermi gas
    • Exercise 6.1: PDF.
    • Exercise 6.2: PDF.
    • Exercise 6.3: PDF.
  • 7. Energy bands
    • Exercise 7.1ab: PDF.
    • Exercise 7.3: PDF.

Last updated: 2026-09-12 21:23 PDT.