Step 1: identify major fields in Physics

- Electromagnetism
- relativity
- astrophysics
- quantum mechanics
- classical mechanics
- thermodynamics

Step 2: identify top derivations associated with each area

- Electromagnetism: Maxwell's equations
- Relativity: Lorentz (time dilation, length contraction)
- astrophysics:
- Quantum mechanics: Schrodinger, Uncertainty
- Classical mechanics: F=ma, conservation of energy and momentum
- thermodynamics: entropy

Step 3:

There are expressions, domains, and notations that need to be included to demonstrate the comprehensive nature of the project and the capability of the framework.

Expressions | Domains | Notation |
---|---|---|

Schrodinger's equation | Quantum | Dirac/bra-ket |

Maxwell's equations | Electromagnetics | differentiation, vectors |

contravariant/covariant | Electrodynamics | Einstein notation |

Navier Stokes | Fluid Mechanics | differentiation, vectors |

mass-energy relation | ||

Special Relativity | ||

Thermodynamics | ||

Uncertainty relation | Quantum Mechanics | |

energy conservation | classical mechanics | |

string theory | ||

wave equation | ||

statistical mechanics | ||

aerodynamics | ||

simple harmonic oscillator |

Other comprehensive lists of "things to know" in Physics

The Physics Derivation Graph has a few pertinent scales:

- topics within physics, ie thermodynamics, quantum mechanics, classical mechanics
- https://en.wikipedia.org/wiki/Outline_of_physics#Branches_of_physics
- https://en.wikiversity.org/wiki/High_school_physics
- major (often named) expressions within a domain, ie "E=mc^2", Schrodinger's equation, Maxwell's equations
- https://en.wikipedia.org/wiki/Physics_equations
- https://en.wikipedia.org/wiki/Category:Equations_of_physics
- https://en.wikipedia.org/wiki/List_of_equations
- https://www.mcat-prep.com/mcat-physics-equations-sheet/
- https://physics.info/equations/
- derivations linking the major expressions
- Derivation of Electromagnetic Waves from Maxwell’s Equations
- Deriving time dependent Schrödinger equation from Wave-Mechanics
- abstract syntax trees of an expression

In this post, I'll focus on finding examples of derivations linking the major expressions

### Useful places to search

- Google Scholar
- Arxiv
- journals for Physics teachers

Useful search string: derivation of equation

### Unsorted results

https://en.wikipedia.org/wiki/ADM_formalismhttps://en.wikipedia.org/wiki/Abraham–Lorentz_force

https://en.wikipedia.org/wiki/Acoustic_wave_equation

https://en.wikipedia.org/wiki/Action-angle_coordinates

https://en.wikipedia.org/wiki/Adiabatic_process

https://en.wikipedia.org/wiki/Angular_momentum

https://en.wikipedia.org/wiki/Angular_momentum_operator

https://en.wikipedia.org/wiki/Appell's_equation_of_motion

https://en.wikipedia.org/wiki/Area_of_a_circle

https://en.wikipedia.org/wiki/Available_energy_(particle_collision)

https://en.wikipedia.org/wiki/Avrami_equation

https://en.wikipedia.org/wiki/Azimuthal_quantum_number

https://en.wikipedia.org/wiki/BET_theory

https://en.wikipedia.org/wiki/Backpropagation

https://en.wikipedia.org/wiki/Ballistic_pendulum

https://en.wikipedia.org/wiki/Beer–Lambert_law

https://en.wikipedia.org/wiki/Bell's_theorem

https://en.wikipedia.org/wiki/Bethe–Salpeter_equation

https://en.wikipedia.org/wiki/Bivector

https://en.wikipedia.org/wiki/Black–Scholes_model

https://en.wikipedia.org/wiki/Bloch_oscillations

https://en.wikipedia.org/wiki/Boltzmann_relation

https://en.wikipedia.org/wiki/Bose–Einstein_statistics

https://en.wikipedia.org/wiki/Braking_distance

https://en.wikipedia.org/wiki/CHSH_inequality

https://en.wikipedia.org/wiki/Capillary_wave

https://en.wikipedia.org/wiki/Catenary

https://en.wikipedia.org/wiki/Causal_dynamical_triangulation

https://en.wikipedia.org/wiki/Causality

https://en.wikipedia.org/wiki/Centimetre–gram–second_system_of_units

https://en.wikipedia.org/wiki/Centripetal_force

https://en.wikipedia.org/wiki/Charge_conservation

https://en.wikipedia.org/wiki/Classical_electron_radius

https://en.wikipedia.org/wiki/Clausius–Clapeyron_relation

https://en.wikipedia.org/wiki/Coefficient_of_restitution

https://en.wikipedia.org/wiki/Collective_noun

https://en.wikipedia.org/wiki/Collision_theory

https://en.wikipedia.org/wiki/Compton_scattering

https://en.wikipedia.org/wiki/Conductance_quantum

https://en.wikipedia.org/wiki/Confidence_interval

https://en.wikipedia.org/wiki/Convolution

https://en.wikipedia.org/wiki/Darcy's_law

https://en.wikipedia.org/wiki/Debye_model

https://en.wikipedia.org/wiki/Derivative

https://en.wikipedia.org/wiki/Diffusion_equation

https://en.wikipedia.org/wiki/Doppler_broadening

https://en.wikipedia.org/wiki/Drag_equation

https://en.wikipedia.org/wiki/Dynamic_mechanical_analysis

https://en.wikipedia.org/wiki/Eddington_luminosity

https://en.wikipedia.org/wiki/Effective_medium_approximations

https://en.wikipedia.org/wiki/Elastic_collision

https://en.wikipedia.org/wiki/Electrodynamic_tether

https://en.wikipedia.org/wiki/Equilibrium_constant

https://en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

https://en.wikipedia.org/wiki/Euler–Maclaurin_formula

https://en.wikipedia.org/wiki/Ewald_summation

https://en.wikipedia.org/wiki/Exponential_decay

https://en.wikipedia.org/wiki/Fermat's_principle

https://en.wikipedia.org/wiki/Feynman_parametrization

https://en.wikipedia.org/wiki/Fick's_laws_of_diffusion

https://en.wikipedia.org/wiki/Fictitious_force

https://en.wikipedia.org/wiki/Fisher_information

https://en.wikipedia.org/wiki/Flory–Huggins_solution_theory

https://en.wikipedia.org/wiki/Fluctuation-dissipation_theorem

https://en.wikipedia.org/wiki/Four-gradient

https://en.wikipedia.org/wiki/Four-momentum

https://en.wikipedia.org/wiki/Fourier_optics

https://en.wikipedia.org/wiki/Freund–Rubin_compactification

https://en.wikipedia.org/wiki/Gaussian_gravitational_constant

https://en.wikipedia.org/wiki/Geiger–Nuttall_law

https://en.wikipedia.org/wiki/Generalizations_of_the_derivative

https://en.wikipedia.org/wiki/Gibbs_free_energy

https://en.wikipedia.org/wiki/Gibbs–Duhem_equation

https://en.wikipedia.org/wiki/Giovanni_Semerano

https://en.wikipedia.org/wiki/Golden_ratio

https://en.wikipedia.org/wiki/Group_velocity

https://en.wikipedia.org/wiki/Group_velocity_dispersion

https://en.wikipedia.org/wiki/Gullstrand–Painlevé_coordinates

https://en.wikipedia.org/wiki/Gyroradius

https://en.wikipedia.org/wiki/Hamilton–Jacobi_equation

https://en.wikipedia.org/wiki/Harmonic_coordinate_condition

https://en.wikipedia.org/wiki/Haynes–Shockley_experiment

https://en.wikipedia.org/wiki/Heat_equation

https://en.wikipedia.org/wiki/Helmholtz_coil

https://en.wikipedia.org/wiki/Helmholtz_decomposition

https://en.wikipedia.org/wiki/Hyperfocal_distance

https://en.wikipedia.org/wiki/Interference_(wave_propagation)

https://en.wikipedia.org/wiki/Ion_acoustic_wave

https://en.wikipedia.org/wiki/Isotropic_radiator

https://en.wikipedia.org/wiki/Kalman_filter

https://en.wikipedia.org/wiki/Killing_vector_field

https://en.wikipedia.org/wiki/Kinetic_energy

https://en.wikipedia.org/wiki/Klein–Gordon_equation

https://en.wikipedia.org/wiki/Kramers–Kronig_relations

https://en.wikipedia.org/wiki/Kramers–Wannier_duality

https://en.wikipedia.org/wiki/Kutta–Joukowski_theorem

https://en.wikipedia.org/wiki/Lamb_shift

https://en.wikipedia.org/wiki/Landau_quantization

https://en.wikipedia.org/wiki/Langmuir_(unit)

https://en.wikipedia.org/wiki/Laplace_expansion_(potential)

https://en.wikipedia.org/wiki/Large_eddy_simulation

https://en.wikipedia.org/wiki/Larmor_formula

https://en.wikipedia.org/wiki/Leibniz_integral_rule

https://en.wikipedia.org/wiki/Length_contraction

https://en.wikipedia.org/wiki/Lie_algebra

https://en.wikipedia.org/wiki/Liénard–Wiechert_potential

https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)

https://en.wikipedia.org/wiki/Linearized_gravity

https://en.wikipedia.org/wiki/Lippmann–Schwinger_equation

https://en.wikipedia.org/wiki/Magic_number_(physics)

https://en.wikipedia.org/wiki/Magnetic_quantum_number

https://en.wikipedia.org/wiki/Mass–energy_equivalence

https://en.wikipedia.org/wiki/Maxwell–Boltzmann_statistics

https://en.wikipedia.org/wiki/Mean_effective_pressure

https://en.wikipedia.org/wiki/Mean_free_path

https://en.wikipedia.org/wiki/Metalloid

https://en.wikipedia.org/wiki/Mooney–Rivlin_solid

https://en.wikipedia.org/wiki/Newton's_theorem_of_revolving_orbits

https://en.wikipedia.org/wiki/Noether's_theorem

https://en.wikipedia.org/wiki/Non-associative_algebra

https://en.wikipedia.org/wiki/Optical_flat

https://en.wikipedia.org/wiki/Optical_theorem

https://en.wikipedia.org/wiki/Orbital_state_vectors

https://en.wikipedia.org/wiki/Parabola

https://en.wikipedia.org/wiki/Parallax

https://en.wikipedia.org/wiki/Parametric_oscillator

https://en.wikipedia.org/wiki/Particle_in_a_spherically_symmetric_potential

https://en.wikipedia.org/wiki/Paschen's_law

https://en.wikipedia.org/wiki/Path_integral_formulation

https://en.wikipedia.org/wiki/Perpendicular_axis_theorem

https://en.wikipedia.org/wiki/Pilot_wave

https://en.wikipedia.org/wiki/Planck's_law

https://en.wikipedia.org/wiki/Planck_particle

https://en.wikipedia.org/wiki/Plasmon

https://en.wikipedia.org/wiki/Poisson–Boltzmann_equation

https://en.wikipedia.org/wiki/Polarization_identity

https://en.wikipedia.org/wiki/Ponderomotive_energy

https://en.wikipedia.org/wiki/Ponderomotive_force

https://en.wikipedia.org/wiki/Potential_energy

https://en.wikipedia.org/wiki/Potential_temperature

https://en.wikipedia.org/wiki/Poynting's_theorem

https://en.wikipedia.org/wiki/Price_equation

https://en.wikipedia.org/wiki/Principal_quantum_number

https://en.wikipedia.org/wiki/Principle_of_maximum_entropy

https://en.wikipedia.org/wiki/Quadratic_equation

https://en.wikipedia.org/wiki/Quartz_crystal_microbalance

https://en.wikipedia.org/wiki/RRKM_theory

https://en.wikipedia.org/wiki/Radian

https://en.wikipedia.org/wiki/Radius_of_gyration

https://en.wikipedia.org/wiki/Rainbow

https://en.wikipedia.org/wiki/Read_(surname)

https://en.wikipedia.org/wiki/Redshift

https://en.wikipedia.org/wiki/Reduced_mass

https://en.wikipedia.org/wiki/Relational_quantum_mechanics

https://en.wikipedia.org/wiki/Richards_equation

https://en.wikipedia.org/wiki/Roche_limit

https://en.wikipedia.org/wiki/Rodrigues'_rotation_formula

https://en.wikipedia.org/wiki/Rotating_wave_approximation

https://en.wikipedia.org/wiki/Rutherford_scattering

https://en.wikipedia.org/wiki/Saha_ionization_equation

https://en.wikipedia.org/wiki/Scale_relativity

https://en.wikipedia.org/wiki/Schrödinger_equation

https://en.wikipedia.org/wiki/Schwinger–Dyson_equation

https://en.wikipedia.org/wiki/Second_law_of_thermodynamics

https://en.wikipedia.org/wiki/Shallow_water_equations

https://en.wikipedia.org/wiki/Shockley_diode_equation

https://en.wikipedia.org/wiki/Spin_connection

https://en.wikipedia.org/wiki/Spin_quantum_number

https://en.wikipedia.org/wiki/Stefan–Boltzmann_law

https://en.wikipedia.org/wiki/Stretch_rule

https://en.wikipedia.org/wiki/String_theory

https://en.wikipedia.org/wiki/Sverdrup_balance

https://en.wikipedia.org/wiki/Taylor's_theorem

https://en.wikipedia.org/wiki/Terminal_velocity

https://en.wikipedia.org/wiki/Tetum_language

https://en.wikipedia.org/wiki/Theorem

https://en.wikipedia.org/wiki/Torque

https://en.wikipedia.org/wiki/Torricelli%27s_equation#Derivation

https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm#Derivation

tag: math

https://en.wikipedia.org/wiki/Tropical_cyclone#Maximum_potential_intensity

tag: weather

https://en.wikipedia.org/wiki/Twomey_effect#Derivation

https://en.wikipedia.org/wiki/Van_der_Waals_equation#Derivation

https://en.wikipedia.org/wiki/Variable-range_hopping#Derivation

https://en.wikipedia.org/wiki/Visibility#Derivation

https://en.wikipedia.org/wiki/Wallis_product#Derivation

tag: math

https://en.wikipedia.org/wiki/Washburn%27s_equation#Derivation

https://en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt_equation#Derivation_from_path_integral

https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_equation#Derivation

https://en.wikipedia.org/wiki/Optical_theorem

https://farside.ph.utexas.edu/teaching/qm/lectures/node87.html

Seismic Wave Equation

http://www.ees.nmt.edu/outside/courses/GEOP523/Docs/waveeq.pdf

tag: PDF

Noether's theorem

https://en.wikipedia.org/wiki/Noether%27s_theorem#Derivations

https://www.youtube.com/watch?v=Rqfj7n5aSwY

https://en.wikipedia.org/wiki/Kalman_filter#Derivations

E=mc2 and F=ma

Ives, Herbert E. (1952), "Derivation of the mass–energy relation", Journal of the Optical Society of America, 42 (8): 540–543, doi:10.1364/JOSA.42.000540 | tag: paywall

On the page http://www.emc2-explained.info/Emc2/Deriving.htm

there's a step which involves https://en.wikipedia.org/wiki/Integration_by_substitution

--> I don't understand the third line of equations. The infinitesimal switches from ds to d(mv), and the integration limit changes.

https://en.wikipedia.org/wiki/Maxwell_relations#Derivation

tag: PDF

Maxwell's equations as presented in Feynman's lectures

Feynman's derivation of Maxwell equations and extra dimensions: https://arxiv.org/abs/hep-ph/0106235

derivation of the time‐dependent convective‐diffusion equation for surfactant transport along a deforming interface

tag: paywall

Derivation of the Continuous-Time Random-Walk Equation

tag: paywall

derivation of the chemical master equation

tag: paywall

Derivation of Kramer's equation, friction coefficient, and macroscopic laws for physisorption

tag: paywall

QUANTUM-MECHANICAL DERIVATION OF AN EQUATION OF STATE OF IRON

tag: PDF

derivation of an equation for predicting minimum spouting velocity - DOI: 10.1002/aic.690040423

tag: paywall

Derivation of the Biot-Savart Law from Ampere's Law Using the Displacement Current

tag: paywall

https://physics.stackexchange.com/questions/67445/is-biot-savart-law-obtained-empirically-or-can-it-be-derived

http://www.wikihow.com/Derive-the-Biot%E2%80%90Savart-Law

### Classical mechanics

https://en.wikipedia.org/wiki/Projectile_motionhttps://en.wikipedia.org/wiki/Trajectory#Derivation_of_the_equation_of_motion

https://en.wikipedia.org/wiki/Wave_equation#Derivation_of_the_wave_equation

https://en.wikipedia.org/wiki/Work_(physics)#Derivation_for_a_particle_in_constrained_movement

Derivation of Kepler's laws: https://physics.stackexchange.com/questions/112668/derivation-of-keplers-laws

https://en.wikipedia.org/wiki/Diffusion_equation#Derivation

Heat and Diffusion Equation in Space and Time

tag: PDF

Derivation of the Diﬀusion Equation

tag: PDF

Derivation of Diffusion Equation

tag: PDF

https://en.wikipedia.org/wiki/Airfoil#Derivation_of_thin_airfoil_theory

Relation between F=ma and Newton's Second Law of Motion

http://winnerscience.com/2013/06/06/derive-relation-f-ma-from-newton-2nd-law-of-motion/

https://physics.stackexchange.com/questions/105460/deriving-f-ma-newtons-second-law-of-motion

http://zonalandeducation.com/mstm/physics/mechanics/momentum/introductoryProblems/momentumSummary2.html

http://www.batesville.k12.in.us/Physics/PhyNet/Mechanics/Momentum/deriving_eqn.htm

Rocket equation

http://my.fit.edu/~dkirk/4262/Lectures/Rocket%20Equation%20Differential%20Form.doc

http://www.pgccphy.net/rec/rec006-rocket.pdf

https://spaceflightsystems.grc.nasa.gov/education/rocket/rktpow.html

http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node103.html

https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation#Derivation

https://en.wikipedia.org/wiki/Derivation_of_the_Navier%E2%80%93Stokes_equations

A New Derivation of Jeffery’s Equation -- DOI: 10.1007/s00021-005-0208-0

tag: paywall, PDF

### Relativity

### Electronics

https://en.wikipedia.org/wiki/M-derived_filter#Derivationkirchoff current law and kirchoff voltage law

tag: PDF

### Thermal, aka statistical, mechanics

https://en.wikipedia.org/wiki/Widom_scalingLocal thermodynamic derivation of Young's equation

tag: paywall, PDF

https://en.wikipedia.org/wiki/Relations_between_heat_capacities#Derivation

https://en.wikipedia.org/wiki/Gibbs%E2%80%93Helmholtz_equation#Derivation

https://en.wikipedia.org/wiki/Gibbs_free_energy#Derivation

Derivation of the Boltzmann principle

tag: PDF

Boltzmann distribution

https://gravityandlevity.wordpress.com/2018/07/14/how-thick-is-the-atmosphere-a-derivation-of-the-boltmzann-distribution/amp/

https://news.ycombinator.com/item?id=17539765

Note on the derivation of the Boltzmann equation from the Liouville equation

tag: paywall, PDF

https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution#Derivation_and_related_distributions

Entropy

tag: PDFhttps://en.wikipedia.org/wiki/Fundamental_thermodynamic_relation

Derivation of the Ideal Gas Law

DOI: 10.1021/ed084p1832

http://homepage.smc.edu/gallogly_ethan/files/ideal%20gas%20law%20derivation.pdf

tag: PDF

http://quantumfreak.com/derivation-of-pvnrt-the-equation-of-ideal-gas/

https://en.wikipedia.org/wiki/Ideal_gas_law#Theoretical

### Quantum Mechanics

https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation#DerivationDeriving time dependent Schrödinger equation from Wave-Mechanics

tag: PDF

Derivation of Schrodinger's equation

tag: arxiv

tag: arxiv

Derivation of Schrödinger's equation from stochastic electrodynamics -DOI: 10.1007/BF00670387

tag: paywall

tag: paywall

Derivation of the Schrödinger Equation from Newtonian Mechanics

tag: paywall, PDF

Covariant Feynman derivation of Schrodinger's equation in a riemannian spacetag: paywall, PDF

tag: paywall, PDF

http://fermatslibrary.com/s/feynmans-derivation-of-the-schrodinger-equation

Derivation of the Dirac equation from a relativistic representation of spin

tag: paywall, PDF

Physical meaning and derivation of Schrodinger and Dirac equations

tag: arxiv

The Dirac Equation

tag: PDF

Particle in a 1D box

https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Quantum_Mechanics/05.5%3A_Particle_in_Boxes/Particle_in_a_1-dimensional_box

http://quantummechanics.ucsd.edu/ph130a/130_notes/node136.html

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/pbox.html

https://en.wikipedia.org/wiki/Particle_in_a_box

### Plasma

Thermodynamic derivation of Saha's equation for a multi-temperature plasmatag: paywall, PDF

Abstract: This thesis establishes a precise mathematical connection between the Einstein equations of general relativity and the incompressible Navier-Stokes equation of fluid dynamics.

see also http://arxiv.org/abs/1101.2451

Relation between uncertainty and the quantum harmonic oscillator

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc4.html

https://www.eng.fsu.edu/~dommelen/quantum/style_a/nt_uprl.html

http://hitoshi.berkeley.edu/221a/coherentstate.pdf

Schrodinger equation and quantum harmonic oscillator

http://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_5.pdf

Schrodinger equation and wave equation

http://physics.stackexchange.com/questions/75363/how-is-the-schroedinger-equation-a-wave-equation

http://www.tcm.phy.cam.ac.uk/~bds10/aqp/handout_foundations.pdf

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