Physics Self-Study

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

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

This page served to demonstrate my understanding in physics, in lieu of an institutional transcript.

It contains my solutions to textbook exercises, signed and dated.

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

Total worked solutions: 316 PDFs.

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: 2026-01-10 11:07 GMT.