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Math Intuition for Quantum Mechanics & Quantum Field Theory
Highest Rated
Rating: 4.6 out of 5(116 ratings)
3,900 students

Math Intuition for Quantum Mechanics & Quantum Field Theory

Quantum Mechanics and Quantum Field Theory
Last updated 3/2026
English

What you'll learn

  • The mathematical intuition for Quantum Mechanics and Quantum field theory
  • How to (intuitively) derive the Schrodinger's equation from the classical theory
  • Quantum operators
  • Quantum states
  • Importance of commutators
  • Derivation of Heisenberg Uncertainty Principle
  • Unitary operators
  • Quantum Tunneling
  • Energy Spectrum of the hydrogen atom
  • How to quantize a Classical Field theory
  • Klein Gordon equation
  • Wick's theorem
  • Time ordering
  • Normal ordering
  • Noether's theorem
  • Properties of the infinitesimal Lorentz transformation
  • Spectrum of the Hamiltonian
  • Scattering cross-section
  • Annihilation and creation operators
  • Causality in quantum field theories
  • Ground state
  • Green functions
  • Schrodinger's picture
  • Heisenberg's picture
  • Interaction picture
  • Theory of Fermions
  • Theory of Bosons
  • Dirac equation
  • Interacting Field theory
  • Feynman diagrams
  • Anomalous magnetic moment

Course content

20 sections151 lectures43h 6m total length
  • Derivation of the energy operator in QM9:41
  • Derivation of the momentum operator in QM18:34

Requirements

  • Special Relativity (for Quantum Field Theory)
  • Fourier Series and Transforms
  • Multivariable Calculus
  • Tensors (for Quantum Field Theory)
  • Complex calculus (for Quantum Field Theory)
  • Classical Physics
  • Probability theory (distributions, probability densities, etc.)

Description

This course aims to mathematically motivate both Quantum Mechanics (QM) and Quantum field Theory (QFT). The first part is devoted to the most important concepts and equations of QM, whereas the second part deals with QFT.

Due to the conceptual and mathematical difficulty of these subjects, some prerequisites to this course are unavoidably required. The student should be familiar with:

1) the Fourier Series and Transform;

2) Multivariable Calculus;

3) Probability theory and random variables;

4)  Classical Physics;

5) Complex Calculus (especially residues and calculation of integrals on a contour), although this is necessary only for some parts of the course devoted to QFT;

6) Special Relativity and tensors for QFT.

Note 1: the first few prerequisites might be enough if you are interested only in the first part of the course, which is related to QM (consider that this course has tens of hours' worth of material, you might be interested only in some parts);

Note 2: I'm more than willing to reply if you have doubts/need clarifications, or -why not- have any recommendations to improve the quality of the course.

Note 3: I will still continue to edit the videos (for example by adding notes) to make the video-lectures as clear as possible.


Some references for the part on QFT are the following:

- Quantum Field Theory, M.Srednicki

- Quantum Field Theory, Itzykson & Zuber

- QFT by Mandl & Shaw

- QFT in a nutshell, A.Zee

- QFT by Ryder, Ramand

- The Quantum Theory of Fields, S.Weinberg

- Gauge Theories in Particle Physics, Aitchison & Z.Hey


Some references for the part on QM:

- Quantum Mechanics: Non-Relativistic Theory, L.D. Landau, E.M. Lifshitz

- Principles of Quantum Mechanics, P.A.M. Dirac

- Introduction to Quantum Mechanics, David J. Griffiths

- Modern Quantum Mechanics, J. J. Sakurai, Jim Napolitano

Who this course is for:

  • Students who desire to develop mathematical intuition for Quantum mechanics and Quantum Field theory