get app
    • Home
    • Udemy
    • Courses
    • Math Intuition for Quantum Mechanics and Quantum Field Theory

    Math Intuition for Quantum Mechanics & Quantum Field Theory

    BY
    Udemy

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

    Brochure Enquire
    Mode

    Online

    Fees

    ₹ 2499

    Quick Facts

    particular details
    Medium of instructions English
    Mode of learning Self study
    Mode of Delivery Video and Text Based

    Course overview

    Math Intuition for Quantum Mechanics & Quantum Field Theory online certification is created by Emanuele Pesaresi - Ph.D. in Mechanics and Advanced Engineering Sciences, which is delivered by Udemy for candidates who want to gain mathematical understanding in quantum field theory and quantum mechanics. Math Intuition for Quantum Mechanics & Quantum Field Theory online course is designed to provide candidates with the resources they need to understand quantum mechanics and quantum field theory mathematically.

    Candidates who are willing to enroll in the Math Intuition for Quantum Mechanics & Quantum Field Theory online classes must have prior knowledge of probability, Fourier series and transforms, multivariate calculus, random variables, physics, special relativity, calculus, and tensors of QFT. This training involves more than 39.5 hours of prerecorded resources which discuss topics like time ordering, normal ordering, anomalous magnetic moment, unitary operator, quantum tunneling, and quantum states, along with major theories related to QFT and QM.

    The highlights

    • Certificate of completion
    • Self-paced course
    • 39.5 hours of pre-recorded video content
    • Learning resources

    Program offerings

    • Online course
    • Learning resources. 30-day money-back guarantee
    • Unlimited access
    • Accessible on mobile devices and tv

    Course and certificate fees

    Fees information
    ₹ 2,499
    certificate availability

    Yes

    certificate providing authority

    Udemy

    Who it is for

    Teacher Scientist Physicist

    What you will learn

    Mathematical skill

    After completing the Math Intuition for Quantum Mechanics & Quantum Field Theory certification course, candidates will develop a deeper comprehension of the concepts of mathematics for an operation involving quantum mechanics and quantum field theory. Candidates will explore concepts and methodologies associated with various theories including Schrodinger's equation, Heisenberg's uncertainty principle, Wick's theorem, Klein Gordon equation, Noether's theorem, Lorentz transformation, Green’s function, theory of Fermions, Dirac equation, Feynman diagrams, theory of Bosons, and interacting field theory. Candidates will also study time ordering, normal ordering, quantum operators, unitary operators, quantum states, quantum tunneling, and anomalous magnetic moments, among other topics in quantum mechanics and field theory.

    The syllabus

    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

    Instructors

    Mr Emanuele Pesaresi

    Mr Emanuele Pesaresi
    Instructor
    Freelancer

    Other Bachelors, Other Masters, Ph.D

    Trending Courses

    Digital Marketing Courses Fashion Design Courses Data Science Courses Interior Design Courses Graphic Designing Courses Cyber Security Courses Nursing Courses Tally Courses Data Analysis Courses Web Designing Courses Artificial Intelligence Courses Ethical Hacking Courses Free Digital Marketing Courses And certifications Free Artificial Intelligence Courses And Certifications Free Data Analysis Courses And Certifications Free Cyber Security Courses And Certifications Free Data Science Courses And Certifications Free Cloud Computing Courses And Certifications Free Python Courses And Certifications Free Fashion And Textiles Courses And Certifications Free Graphic Designing Courses And Certifications Free Web Designing Courses And Certifications

    Popular Courses

    General Management Courses Public Health Courses Teaching and Education Courses Financial Management Courses Web Development Courses Mathematics Courses Cyber Security Courses Data Science Courses Programming Courses Digital Marketing Courses Leadership Courses Mechanical Engineering Courses Explore all courses

    Popular Platforms

    upGrad Courses Udemy Courses Edx Courses Coursera Courses Swayam Courses Futurelearn Courses Mindmajix Technologies Courses Vskills Courses IIT Kharagpur Courses Emeritus Courses IIT Madras Courses MSBM Courses Explore all platforms

    Learn more about the Courses

    10 Reasons to Enrol Yourself in a Digital Marketing Course 8 Must-Have Skills for AWS Cloud Architects Planning to Upskill Yourself? Enrol for a Program in Data Science 25+ Tips for Improving Your Graphic Design Skills Top Universities in India Offering Cyber Security Courses 15+ Courses for Learning Data Mining How to Make a Career in the Field of Artificial Intelligence Top 10 Benefits Of Holding A Certification In Business Intelligence Which are the best certification courses for Photography in India A Beginner's Guide to Pursue Python Programming Want to Pursue a Career in Blockchain Technology? Here is all that you need to Know How Entrepreneurs Can Use Machine Learning to Make their Business Successful? The Scope of Artificial Intelligence in India Top 10 Online Courses for Travel Lovers 10 Best Certification Courses After Hospital and Healthcare Management
    Providers
    Close

    Download the Careers360 App on your Android phone

    Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

    Careers360 App
    150M+ Students
    30,000+ Colleges
    500+ Exams
    1500+ E-books