- Adjoint Dirac equation
- Adjoint Dirac equation: explicit solutions
- Anticommutators, creation and annihilation operators in the Dirac equation
- Coordinate transformations in classical field theory
- Coupled oscillators in terms of creation and annihilation operators; phonons
- Creation and annihilation operators for the 3-d harmonic oscillator
- Creation and annihilation operators in the harmonic oscillator
- Creation and annihilation operators in the harmonic oscillator: a few theorems
- Creation and annihilation operators: commutators and anticommutators
- Creation and annihilation operators: normalization
- Creation and destruction operators for a free scalar field
- Delta function: a couple of alternative derivations
- Dirac equation
- Dirac equation as four coupled differential equations
- Dirac equation in quantum field theory: Lagrangian density
- Dirac equation in relativistic quantum mechanics: summary
- Dirac equation: 4 solution vectors
- Dirac equation: adjoint solutions
- Dirac equation: conserved probability current
- Dirac equation: inner products of spinors
- Dirac equation: matrix properties
- Dirac equation: non-relativistic limit
- Dirac equation: orthogonality of solutions
- Dirac equation: positive probabilities and negative energies
- Dirac equation: spin of a moving particle
- Dirac equation: spin of a particle at rest
- Dirac equation: spinors near the speed of light
- Dirac equation: the gamma matrices
- Dirac spin operator in quantum field theory
- Discrete Fourier transforms
- Eigenfunctions of position and momentum; unit operators
- Eigenspinors of the Pauli spin matrices
- Euler-Lagrange equations for particle & field theories; Lagrangian density
- Euler-Lagrange equations: a couple of examples
- Fermat's principle of least time and Snell's law
- Fermion wave functions; the Slater determinant
- Feynman propagator as a contour integral
- Feynman propagator as a single real integral
- Feynman propagator for scalar fields
- Feynman propagator in terms of commutators
- Feynman propagator: from commutator to integral
- Field operators for the infinite square well
- Free scalar Hamiltonian as an integral of the Hamiltonian density
- From mattress to field
- Functional derivative: a 4-dimensional example
- Functional derivatives and the Lagrangian
- Functional derivatives: more examples
- Functionals and functional derivatives
- Gaussian integrals: averages of powers of x
- Gaussian integrals: averages over matrix components and the Wick contraction
- Gaussian integrals: single variable & matrix exponents
- Hamilton's equations and Poisson brackets
- Hamilton's equations for relativistic fields; conjugate momentum
- Hamilton's equations of motion in classical field theory
- Hamiltonian density for the Dirac equation
- Hamiltonian for the Dirac equation
- Harmonic oscillator ground state from annihilation operator
- Helicity operator in the Dirac equation
- Klein-Gordon equation
- Klein-gordon equation - derivation and continuity equations
- Klein-Gordon equation for fields; derivation from the Lagrangian
- Klein-Gordon equation from the Heisenberg picture
- Klein-Gordon equation with anticommutators
- Klein-Gordon equation: commutators
- Klein-Gordon equation: continuous solutions
- Klein-gordon equation - nonrelativistic limit
- Klein-Gordon equation: orthonormality of solutions
- Klein-Gordon equation: plane wave solutions
- Klein-Gordon equation: probability density and current
- Lagrangian for inhomogeneous Maxwell's equations
- Lagrangian for the SchrÃ¶dinger equation
- Lagrangians and the principle of least action
- Lagrangians for elastic media
- Lorentz transformation as product of a pure boost and pure rotation
- Lorentz transformation for infinitesimal relative velocity
- Lorentz transformations and the special linear group SL(2,C)
- Lorentz transformations as 2x2 matrices
- Lorentz transformations as rotations
- Maxwell's equations using the electromagnetic field tensor
- Momentum of a free scalar Klein-Gordon field
- Momentum of particles in a Dirac field
- Natural units
- Natural units: the muon lifetime
- Noether's theorem
- Noether's theorem and conservation laws
- Noether's theorem and conservation of angular momentum
- Noether's theorem and conservation of energy and momentum
- Notation for Relativistic Quantum Mechanics
- Number operator
- Occupation number representation; delta function as a series
- Path integrals in quantum mechanics
- Poisson brackets and Hamilton's equations of motion
- Poisson brackets in classical field theory
- Probability density in a Klein-Gordon field
- Quantum field theory representation of non-relativistic quantum mechanics
- Real Klein-Gordon fields
- Second quantizing a single-particle operator
- Second quantizing operators - examples
- Second quantizing the tight-binding hamiltonian
- Steepest descent and the classical limit of quantum mechanics
- Unitary transformations and the Heisenberg picture
- Vacuum energy in the free Klein-Gordon field