Math Intuition for Quantum Mechanics & Quantum Field Theory

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Acquire a thorough understanding of the fundamentals and functionality of quantum field theory and quantum mechanics.

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                                    Medium of instructions
                                    English

                                    Mode of learning
                                    Self study

                                    Mode of Delivery
                                    Video and Text Based

Operators in Quantum Mechanics

Derivation of the energy operator in QM
Derivation of the momentum operator in QM

Schrodinger equation, States, Eigenstates, Hermitian operators

Construction of the Schrodinger equation in QM
Eigenstates and normalized states
Importance of Hermitian operators

Commutator, Uncertainty principle, Unitary operators

Commutator and uncertainty principle
Uncertainty principle for position and momentum
Unitary operators and time evolution of a system

Quantum tunneling

intro to quantum tunneling
Rectangular potential barrier (classical physics)
Solving the QM problem with the method of separation of variables
Solution for x less than 0
Solution for x in the interval [0, L]
Solution for x greater than L
Constraints on the solutions and definition of the transmission coefficient
Derivation of the transmission coefficient

Derivation of the energy spectrum of the hydrogen atom

Intro to this section
Hydrogen-like atoms
Hamiltonian of a hydrogen-like atom
More on potential energy and how to find the spectrum
Separation of variables in the Schrodinger equation
Time independent Schrodinger equation in spherical coordinates
Separating the variables in the time-independent Schrodinger equation
Radial Schrodinger equation
Working on the radial Schrodinger equation
Solution to the radial Schrodinger equation
Derivation of the discrete energy spectrum

The need for Quantum Field theory, review of Classical field theory

Reconciling Quantum Mechanics with Special Relativity
Review of Classical Field Theory part 1
Review of Classical Field Theory part 2

Noether's theorem, Complex scalar field, symmetries, Energy momentum tensor

Klein Gordon equation derived from Classical field theory
Noether's theorem
Example of complex scalar field & more on Noether's theorem
Symmetry with respect to coordinate and field transformation
Energy momentum tensor, orbital angular momentum, intrinsic angular momentum
Derivation of important properties of the infinitesimal Lorentz transformation

Quantization of a real scalar field

Quantization of a Classical Field part 1
Quantization of a Classical Field part 2
Derivation of the spectrum of the Hamiltonian
Annihilation and creation operators to determine the spectrum of the Hamiltonian
Ground state and construction of states with a certain number of quanta
Definition of the number operator
Causality of space-like events part 1
Causality of space-like events part 2
Causality of space-like events part 3, an important property of Dirac delta
Causality of space-like events part 4
Green function of the Klein Gordon field part 1
Green function of the Klein Gordon field part 2
Vacuum expectation, Propagator, Time Ordering
Complex Klein Gordon field

Interactions in Quantum Field Theory

Interacting Classical Field theory part 1
Interacting Classical Field Theory part 2
Heisenberg's picture and Schrodinger's picture
Interaction picture
Interacting field theory part 1
Interacting field theory part 2
Interacting Field theory, S matrix
Rewriting time ordering in the S matrix part 1, proof of Hausdorff formula
Rewriting time ordering in the S matrix part 2
Relation between Normal and Time ordered products
Wick's theorem

Interactions: Scattering cross section, LSZ formula

Scattering cross section part 1
Scattering cross section part 2
Scattering cross section part 3
LSZ formula part 1
LSZ formula part 2
LSZ formula part 3
LSZ formula part 4
LSZ formula part 5
LSZ formula part 6
LSZ formula part 7

Quantization of the Electromagnetic Field

Quantization of the E.M. field part 1
Quantization of the E.M. field part 2
Quantization of the E.M. field part 3
Quantization of the E.M. field part 4
Quantization of the E.M. field part 5
Quantization of the E.M. field part 6

Spin in Quantum Mechanics and Quantum Field Theory

Stern-Gerlach experiment
Intrinsic Angular Momentum in QM (spin) part 1
Intrinsic Angular Momentum in QM (spin) part 2
Pauli matrices, spinors
Unitary operators, Lorentz transformations, angular momenta in QFT part 1
Unitary operators, Lorentz transformations, angular momenta in QFT part 2
Unitary operators, Lorentz transformations, angular momenta in QFT part 3
Unitary operators, Lorentz transformations, angular momenta in QFT part 4
Commutator between a scalar field and angular momentum
Commutator between a vector field and angular momentum

Fermion quantization, Dirac equation

Spinors in 4 dimensions part 1
Spinors in 4 dimensions part 2
Spinors in 4 dimensions part 3
Invariant quantities and Fermion fields
Derivation of the Dirac equation
Hamiltonian density and conserved quantities for the Dirac field
Construction of solutions of the Dirac equation part 1
Construction of solutions of the Dirac equation part 2
Quantization of the Fermion field
Important properties of the Fermion field part 1
Important properties of the Fermion field part 2, charge operator
Parity operator
Spin of the Dirac field part 1
Spin of the Dirac field part 2

Interaction between the Dirac field and the E.M. field

Interaction of Dirac field and E.M. field
S matrix elements, interacting particles, diagrams
Amplitudes and diagrams of processes
Why 1st order terms in the S matrix do not give contribution
Calculation of amplitudes of 2nd order processes
Feynman Rules part 1
Feynman Rules part 2

Calculation of propagators

Fermion propagator derivation 1
Fermion propagator derivation 2 part 1
Fermion propagator derivation 2 part 2
Derivation of the photon propagator
Boson propagator derived from the vacuum expectation

Compton scattering cross section

Compton's Scattering cross section part 1
Compton's Scattering cross section part 2
Compton's Scattering cross section part 3
Compton's Scattering cross section part 4
Compton's Scattering cross section part 5
Compton's Scattering cross section part 6
Compton's Scattering cross section part 7
Compton's Scattering cross section part 8
Compton's Scattering cross section part 9

Higher order contributions to Feynman diagrams

Higher order Feynman diagrams, vertex correction part 1
Vertex correction part 2
Vertex correction part 3
Landè g factor obtained through vertex correction
Vertex correction of a higher order process part 1
Vertex correction of a higher order process part 2
Vertex correction of a higher order process part 3
Vertex correction of a higher order process part 4, Wick rotation
Vertex correction of a higher order process part 5, Landè g factor
Electron self-energy part 1
Electron self-energy part 2

Appendix

Appendix: Exponential form of operators
Appendix: Dirac equation derived intuitively
Proof that the average kinetic energy of a quantum system is non-negative
Classical mechanics derived from the Schrodinger Equation

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