Math Intuition for Quantum Mechanics & Quantum Field Theory
This course provides a mathematical foundation for understanding Quantum Mechanics and Quantum Field Theory. It covers important concepts and equations, with prerequisites including Fourier Series, Multivariable Calculus, Probability Theory, Classical Physics, Complex Calculus, and Special Relativity. Recommended references are provided for further study. Ideal for students seeking to develop mathematical intuition in these subjects.
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
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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’ll still keep editing the videos (for example by adding notes) to make the video-lectures as clear as possible.
The 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
Who this course is for:
- Students who desire to develop mathematical intuition for Quantum mechanics and Quantum Field theory
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