Math Intuition for Quantum Mechanics & Quantum Field Theory from Udemy

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

What's inside

Learning objectives

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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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
Show more
Show less

Syllabus

Why Operators are needed in Quantum Mechanics

Derivation of the energy operator in QM

Derivation of the momentum operator in QM

How to derive (intuitively) the Schrodinger equation, how to define States, Eigenstates, and the importance of Hermitian operators

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Read about what's good

what should give you pause

and possible dealbreakers

Covers the derivation of the Schrodinger equation, offering a deep dive into the fundamental principles that govern quantum systems

Explores the mathematical underpinnings of quantum mechanics and quantum field theory, which are essential for advanced study and research

Requires familiarity with Fourier series, multivariable calculus, and probability theory, indicating an advanced level of mathematical sophistication

Examines the Klein-Gordon equation and Wick's theorem, which are pivotal concepts in understanding relativistic quantum mechanics

Delves into the intricacies of interacting field theory and Feynman diagrams, which are essential tools for calculating particle interactions

Requires knowledge of special relativity and tensors for the quantum field theory portion, suggesting a focus on advanced theoretical physics

Reviews summary

Mathematical intuition for qm and qft

According to students, this course is highly recommended for those with a strong mathematical background, providing excellent insights and deep explanations into the mathematics of Quantum Mechanics and Quantum Field Theory. Learners praise its rigor and clarity, noting how it effectively builds intuition and breaks down complex ideas. The instructor is highly regarded for being knowledgeable, passionate, and responsive. However, students universally emphasize the need for significant prerequisites and a very high level of mathematical maturity, making it unsuitable for beginners. Some mention that the pace can be fast, particularly in the QFT section, which is sometimes seen as less strong than the QM part.

Instructor is knowledgeable, passionate, and responsive.

"The instructor is very helpful and responsive."

"The instructor is clearly knowledgeable and passionate."

"The instructor is very clear."

"Instructor is top-notch."

Breaks down complex concepts with rigor.

"explains the topics with rigor and clarity."

"The explanations are deep and cover the material thoroughly."

"...covers a significant amount of material with great clarity."

"...the way complex ideas were broken down."

Provides deep mathematical intuition and derivations.

"Absolutely brilliant course! The mathematical derivations were crystal clear, building intuition step by step."

"This course is exactly what I was looking for! It focuses on the mathematical side, which is crucial for understanding these complex fields."

"Fantastic course that delivers on its promise of mathematical intuition. I appreciated the step-by-step derivations..."

"One of the best online courses I've taken on advanced physics. The focus on mathematical intuition is unique and incredibly helpful."

Course moves quickly, particularly in the QFT section.

"Some parts felt a bit rushed, particularly in the QFT section."

"The QFT part is dense and could benefit from more examples or slower pacing."

"It moves very fast."

Demands significant prior mathematical and physics knowledge.

"Essential prerequisites are needed, especially for the QFT part."

"Requires a solid background, but if you have it, this course is invaluable."

"Highly recommended for anyone with a strong math background interested in QM/QFT."

"I struggled with this course. Even though I met the prerequisites, I found the explanations sometimes difficult to follow."

"Way over my head. It assumes a level of comfort with advanced math I simply don't have, despite having taken university calculus."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Math Intuition for Quantum Mechanics & Quantum Field Theory with these activities:

Review Multivariable Calculus

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Strengthen your understanding of multivariable calculus, which is essential for understanding concepts in both Quantum Mechanics and Quantum Field Theory.

Browse courses on Multivariable Calculus

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Review partial derivatives and gradients.
Practice calculating line and surface integrals.
Study vector fields and their properties.

Brush up on Fourier Transforms

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Revisit Fourier Series and Transforms, as they are fundamental tools used throughout Quantum Mechanics and Quantum Field Theory.

Browse courses on Fourier Transform

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Review the definition of Fourier Series.
Practice calculating Fourier Transforms of common functions.
Understand the properties of Fourier Transforms.

Read 'Quantum Mechanics' by David Griffiths

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Supplement your learning with a comprehensive textbook on Quantum Mechanics to gain a deeper understanding of the core concepts.

View Introduction to Electrodynamics on Amazon

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Read assigned chapters before each corresponding lecture.
Work through the example problems in the book.
Attempt the end-of-chapter problems for practice.

Four other activities

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Show all seven activities

Participate in weekly study groups

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Collaborate with peers to discuss challenging concepts and problem-solving strategies in Quantum Mechanics and Quantum Field Theory.

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Form a study group with classmates.
Review lecture notes and discuss key concepts.
Work through practice problems together.

Solve Quantum Mechanics Problems

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Practice applying theoretical knowledge by solving a variety of problems related to quantum operators, states, and tunneling.

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Find problem sets online or in textbooks.
Attempt to solve problems independently.
Compare solutions with peers or consult solution manuals.

Study 'Quantum Field Theory in a Nutshell' by A. Zee

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Deepen your understanding of Quantum Field Theory with a book that emphasizes physical intuition and provides a broader perspective.

View Einstein Gravity in a Nutshell on Amazon

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Read assigned chapters after each corresponding lecture.
Focus on understanding the physical interpretations.
Work through the exercises to test your understanding.

Create Feynman Diagrams

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Solidify your understanding of interacting field theory by drawing Feynman diagrams for various processes.

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Review the rules for drawing Feynman diagrams.
Choose a specific interaction to analyze.
Draw the corresponding Feynman diagrams.
Explain the physical meaning of each diagram.

Career center

Learners who complete Math Intuition for Quantum Mechanics & Quantum Field Theory will develop knowledge and skills that may be useful to these careers:

Theoretical Physicist

Theoretical physicists develop mathematical models and theories to explain the physical world. This course, *Math Intuition for Quantum Mechanics & Quantum Field Theory*, helps deepen your understanding of the mathematical concepts underpinning quantum mechanics and quantum field theory, which is essential for success as a theoretical physicist. The course explores the derivation of essential equations, quantum operators, quantum states, and the importance of commutators. By learning about the Klein Gordon equation, Wick's theorem, time ordering, normal ordering, and the properties of Lorentz transformation, you will be better able to tackle complex problems in theoretical physics, propose new theories, and contribute to our understanding of the universe at its most fundamental level. Theoretical physicists may find the syllabus useful, as it provides a framework for deriving the spectrum of the Hamiltonian.

See salaries and explore the career path for Theoretical Physicist

Computational Physicist

Computational physicists use computer simulations to solve complex physics problems. This course, *Math Intuition for Quantum Mechanics & Quantum Field Theory*, provides a basis of the mathematical and theoretical knowledge necessary to develop and interpret these simulations. Proficiency with quantum operators, quantum states, and the Schrödinger equation, as covered in this course, is useful for modeling quantum systems. Furthermore, the exploration of Quantum Field Theory concepts, such as Green's functions and Feynman diagrams, enables computational physicists to simulate particle interactions and other complex phenomena. The theory of Bosons and Theory of Fermions are especially helpful.

See salaries and explore the career path for Computational Physicist

Quantum Computing Researcher

A quantum computing researcher works on developing new quantum algorithms and hardware. This is a career where understanding the underlying mathematical principles is paramount. This course, *Math Intuition for Quantum Mechanics & Quantum Field Theory*, helps build the crucial mathematical foundation needed to grasp the concepts of quantum mechanics, quantum operators, and quantum states. The course offers a review of linear algebra, quantum mechanics, quantum field theory, classical physics, special relativity, and tensors for Quantum Field Theory, equipping you with the necessary tools to model and analyze quantum systems, develop quantum algorithms, and contribute to the advancement of quantum computing technologies. The learning objectives, like Heisenberg's picture and Schrodinger's picture, may be useful for researchers.

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Mathematical Modeler

Mathematical modelers create and analyze mathematical models to solve problems in various fields, including physics, engineering, and finance. This course, *Math Intuition for Quantum Mechanics & Quantum Field Theory*, directly applies to the skills needed to model physical systems at the quantum level. A mathematical modeler may find the knowledge of quantum operators, unitary operators, and the Schrödinger equation as a starting point. The advanced topics in quantum field theory, such as Wick's theorem and Feynman diagrams, allows for even more sophisticated models of particle interactions. As a mathematical modeler, the learning objectives from the course provide a framework for solving a wide range of problems.

See salaries and explore the career path for Mathematical Modeler

Quantum Engineer

Quantum engineers apply the principles of quantum mechanics to develop new technologies and devices. This course, *Math Intuition for Quantum Mechanics & Quantum Field Theory,* helps build a strong grasp of the mathematical concepts underpinning quantum mechanics needed to design and implement practical quantum systems. Quantum engineers will benefit from the course's coverage of quantum operators, quantum states, and the Heisenberg Uncertainty Principle, which are foundational to quantum engineering. The exploration of quantum field theory, including topics such as annihilation and creation operators, may be helpful for engineers working on advanced quantum technologies. By studying scattering cross-sections from the syllabus, one can apply the knowledge to real-world problems.

See salaries and explore the career path for Quantum Engineer

Research Scientist

Research scientists design and conduct experiments, analyze data, and publish findings in various fields, including physics and materials science. This course, *Math Intuition for Quantum Mechanics & Quantum Field Theory*, helps to develop the strong analytical and mathematical skills necessary to succeed in this role. The course covers topics such as quantum operators, quantum states, the Heisenberg Uncertainty Principle, and quantum tunneling. Furthermore, the deep dive into quantum field theory, including Wick's theorem, time ordering, and Feynman diagrams, may be useful for research scientists working on cutting-edge experiments involving quantum phenomena. The course may prepare scientists to interpret experimental results, develop new research methodologies, and contribute to scientific breakthroughs.

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Mathematics Professor

A mathematics professor teaches mathematics courses at the university level and performs research in a specific area of mathematics. This course, *Math Intuition for Quantum Mechanics & Quantum Field Theory*, helps to strengthen understanding of the mathematical foundations of quantum mechanics and quantum field theory. This will be valuable both in teaching related courses and in pursuing research in areas where mathematics intersects with physics. The course's coverage of topics like quantum operators, unitary operators, and the derivation of the Schrödinger equation helps provide a deeper and more intuitive understanding of the material, enabling a mathematics professor to convey these complex topics more effectively to students. The professor can also use these skills in his or her original research.

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Physics Teacher

Physics teachers educate students in the principles of physics at the high school or college level. This course, *Math Intuition for Quantum Mechanics & Quantum Field Theory*, may be useful to enhance your understanding of advanced physics concepts, enabling you to teach more effectively and inspire students. The course's coverage of quantum mechanics, quantum field theory, and related mathematical techniques may be useful for teachers. Physics teachers may find the derivation of essential equations, quantum operators, and the Heisenberg Uncertainty Principle to be particularly beneficial, providing them with a deeper understanding of the subject matter.

See salaries and explore the career path for Physics Teacher

Optical Engineer

Optical engineers design and develop optical systems and devices, such as lasers, sensors, and imaging systems. This course, *Math Intuition for Quantum Mechanics & Quantum Field Theory,* helps build a foundation in the mathematical and physical principles underlying optics and photonics. The course's exploration of quantum mechanics and quantum field theory helps to understand the behavior of light at a fundamental level. The study of quantum operators, quantum states, and the interaction of light with matter may be useful for optical engineers. The course may be helpful to design and optimize optical systems, develop new optical materials, and create innovative optical devices.

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Data Scientist

Data scientists analyze large datasets to extract meaningful insights and develop predictive models. While seemingly disparate, the mathematical rigor developed in this course, *Math Intuition for Quantum Mechanics & Quantum Field Theory*, may be beneficial for a data science career, especially in fields dealing with complex systems or simulations. Reviewing the Fourier series and transform, multivariable calculus, probability theory, and complex calculus may help to formulate and test hypotheses, build sophisticated models, and effectively communicate findings to stakeholders. Knowledge of Quantum Mechanics could be applicable for specialized roles in areas like financial modeling or materials discovery.

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Aerospace Engineer

Aerospace engineers design, develop, and test aircraft and spacecraft. This course, *Math Intuition for Quantum Mechanics & Quantum Field Theory,* may not be directly applicable to the day-to-day tasks of most aerospace engineers, it helps develop a strong foundation in mathematical and physical principles that may be valuable in specialized areas. For example, the knowledge of quantum mechanics could be relevant in developing advanced sensors or propulsion systems. The course's coverage of topics like the Schrödinger equation and quantum tunneling may be useful to solve complex engineering challenges. Furthermore, the acquired mathematics from the syllabus may be beneficial in other aspects of the job.

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Software Developer

Software developers design and build software applications. Although this course, *Math Intuition for Quantum Mechanics & Quantum Field Theory*, may not be directly applicable to most software development roles, it helps develop analytical and problem-solving skills that might be useful in specialized areas such as developing simulation software for scientific research or optimizing algorithms for complex calculations. The course's focus on mathematical rigor and theoretical understanding of quantum mechanics may be useful to learn new technologies. Software Developers may benefit from a review of multivariable calculus and complex calculus.

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Machine Learning Engineer

Machine learning engineers develop and implement machine learning algorithms and systems. While this course, *Math Intuition for Quantum Mechanics & Quantum Field Theory,* is not directly related to machine learning, it may help cultivate a strong mathematical foundation that may be useful in certain specialized areas of machine learning research. In particular, the course's coverage of linear algebra, calculus, and probability theory are relevant to the mathematical underpinnings of many machine learning algorithms. The course may be useful to explore advanced topics such as quantum machine learning. Developers may find reviewing the Fourier series beneficial.

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Financial Analyst

Financial analysts evaluate financial data, provide investment recommendations, and manage financial risk. While this course, *Math Intuition for Quantum Mechanics & Quantum Field Theory*, is not directly related to finance, it may help develop strong quantitative and analytical skills. A background in mathematics and physics, as provided by this course, may be useful in developing sophisticated financial models or analyzing complex market dynamics. However, most financial analysis roles require specific knowledge of finance and economics, which are not covered in this course. A financial analyst may benefit from a review of probability theory.

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Biostatistician

Biostatisticians apply statistical methods to solve problems in biology and medicine. While this course, *Math Intuition for Quantum Mechanics & Quantum Field Theory* is not directly relevant to biostatistics, it may help develop strong mathematical and analytical skills that may be transferrable. The course's coverage of multivariable calculus, probability theory, and random variables helps to develop logical reasoning abilities. The course may be useful to learn how to approach complex problems and develop mathematical models, which may be beneficial in any field of quantitative analysis. Biostatisticians may find the section on theory of probability useful.

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Math Intuition for Quantum Mechanics & Quantum Field Theory

What's inside

Learning objectives

Syllabus

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Mathematical intuition for qm and qft

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