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CM-Mod04 :: Hamiltonian Formulation

Node id: 2553page

This section hs problems on Hamiltonian formulation ofclassical mechanics.

kapoor's picture 20-02-08 16:02:01 n

CM-Mod07 :: S:mall Oscillations

Node id: 2347page
kapoor's picture 20-02-08 16:02:01 n

CM-Mod08 :: Motion in Non-Inertial Frames

Node id: 2346page
kapoor's picture 21-05-21 01:05:12 n

CM-Mod09 Rigid BodyDynamics

Node id: 2206page
kapoor's picture 20-02-08 16:02:01 n

CM-Mod10 Canonical Transformations

Node id: 1955page
kapoor's picture 20-02-08 16:02:01 n

CM-Mod11 :: Hamilton Jacobi Theory

Node id: 3303page

Obtain solution of the free particle problem in two dimensions using Hamilton Jacobi equation and obtain expression for the Hamilton's principal function.

kapoor's picture 20-02-08 16:02:01 n

CM02 Lagrangian Form of Dynamics (ProbSets)

Node id: 901page
kapoor's picture 19-12-28 03:12:44 n

CM05 Solution of Equations of Motion (ProbSets)

Node id: 903page
kapoor's picture 19-12-28 03:12:40 n

CM@HCU :: Tutorial I

Node id: 3065page

Assistance for Classical Mechanics Tutorial-I

 

Click to go back to the Tutorial Page

kapoor's picture 22-08-26 12:08:18 n

Collection of Clusters ---- Resource for Learning by a Topic

Node id: 4176collection

About  clusters : A number of things of same sort gathered together or growing together.

This collection has loosely connected, many times overlapping resources arranged according a chosen topics.

Dirac Delta function

 

Green Function

  1. Basic Definition A simple example
  2. Calculating Green Function
  • Using Fourier Transform
  • Free Particle Schrodinger Equation
  • Green Function for Klein Gordon Equation
  • Eigenfunction Expansion
  • Separation of Variables; Example from electrodynamics
  • Uniqueness Theorem; Method of Images
  • Applications
    Converting to an integral equation
    Boundary Value Problems in EM Theory
    Relation to Energy Eigenvalues and Eigenfunctions
  • AND MORE
  •  Vectors  and Tensors

    Vectors --- by ---- John Peacock  Good Introduction for Newbies

    What is a tensor --- by  --- Johann Colombano-Rut Good Introduction for Newbies

    kapoor's picture 21-05-20 04:05:25 n

    Collection of Packs for Newbies

    Node id: 5010multi_level_page

    1: Learning, 2:Problem Solving,

    Quantum Field Theory

    1

    Learning Packs

    • Classical Fields, Lagrangian, Hamiltonian and  Poisson Brackets;Symmetries and Conservation Laws, Noether's Theorem
    • Interaction Picture, Fermi golden rule, S matrixExamples from Quantum Mechanics.
    • The Inhomogeneous Lorentz Group
    • Second Quantization of Schrodinger Field
    • Klein Gordon Field
    • Dirac equation
    • Electromagnetic Field
    • SU(2) group and Yang Mills Field
    • Interaction Hamiltonian, Lorentz invariance, Discrete symmetries
    • S-matrix, Causality and Unitarity. Covariant Perturbation theory             
    • Green functions and Causal propagators
    • Time ordered products and Wick's theorem, 
    • Feynman diagrams, Feynman Rules; More examples of computation of cross sections and life times
    • Higher Orders in Perturbation Theory            

    2

     Problem Solving Packs 

    • Classical Fields, Lagrangian, Hamiltonian and  Poisson Brackets;Symmetries and Conservation Laws, Noether's Theorem
    • Interaction Picture, Fermi golden rule, S matrixExamples from Quantum Mechanics.
    • The Inhomogeneous Lorentz Group
    • Second Quantization of Schrodinger Field
    • Klein Gordon Field
    • Dirac equation
    • Electromagnetic Field
    • SU(2) group and Yang Mills Field
    • Interaction Hamiltonian, Lorentz invariance, Discrete symmetries
    • S-matrix, Causality and Unitarity. Covariant Perturbation theory             
    • Green functions and Causal propagators
    • Time ordered products and Wick's theorem, 
    • Feynman diagrams, Feynman Rules; More examples of computation of cross sections and life times
    • Higher Orders in Perturbation Theory            

    Quantum Mechanics

    1

    Learning Packs

    QM01-Classical Theories Revisited

    2

     Problem Solving Packs

    • QM01-Classical Theories Revisited
    • QM02-A Quick Review of Vector Spaces
    • QM03-Inner Product Spaces
    • QM04-Infinite Dimensional vector spaces
    • QM05-30 years that shook Physics
    • QM06-Postulates of Quantum Mechanics
    • QM07-Canonical Quantization
    • QM08-Eigenvalues Using Commutators
    • QM09-Time Development
      • QM09/LEC-01 Time Evolution of Quantum Systems-I
      • QM09/LEC-02 Heisenberg Picture of Time Evolution
      • QM09/LEC-03 Time Evolution of Quantum Systems-II
    • QM10 Coordinate and Momentum Representation
      • QM10/LEC-01 Introduction to Representations
      • QM10/LEC-2 Coordinate and Momentum Representation
      • QM10/LEC-03 Change of Representation
    • QM11 Time Dependent Schrodinger Equation 
      • QM11/LEC-01 Road to wave Mechanics — Time Dependent Schrodinger Equation
      • QM11/LEC-02 Schrodinger Equation in Coordinate Representation
      • QM11/LEC-03 Solution of Schrodinger Equation in Coordinate Representation
    • Free Particle and Particle in Box
    • Energy Eigenvalue Problems in One Dimension
    • Reflection and Transmission
    • Problems in Two Dimensions
    • Spherically Symmetric Potential Problems
    • Angular Momentum in Quantum Mechanics
    • Scattering -- Three Dimensions
    • Method of Partial Waves
    • Spin and Identical Particles
    • Variation Method
    • WKB Approximation
    • Time Independent Perturbation Theory
    • Approximation Methods for Time Dependent Problems
    • Semi-Classical Theory of Radiation
    • Quantum Hamilton Jacobi Scheme
    • Foundations of Quantum Mechanics
    • Quantum Information
    • Atomic Physics
    • Molecular Physics
    • Nuclear Physics
    • Elementary Particle Physics
    • Relativistic Quantum Mechanics
    • Second Quantization
    • Symmetries in Classical and Quantum Mechanics
    • Applications of Group Theory in Quantum Mechanics
    • Formal Theory of Scattering

     

     

    AK-47's picture 21-12-02 10:12:17 n

    Collection of Video and Animation Links for Class Room

    Node id: 4173collection

    Classical Mechanics

    Small Oscillations

     

    kapoor's picture 21-05-20 04:05:31 n

    Comments embedded in array of equations

    Node id: 253page
    kapoor's picture 19-12-28 03:12:19

    Commutator

    Node id: 283page
    kapoor's picture 19-12-28 03:12:19

    Complete Orthonormal Sets

    Node id: 812page
    kapoor's picture 19-12-28 03:12:51 n

    Complex Variables

    Node id: 5619forum
    kapoor's picture 22-08-07 13:08:52

    Complex Variables

    Node id: 2989page
    kapoor's picture 22-08-17 12:08:50 n

    Complex Variables --- Principles and Problem Sessions :: Top-Page

    Node id: 2436page

    This section of the contents will have solutions to Problems in Part-II of the book

    A. K. Kapoor, "Complex Variables --Principles and Problem Sessions"
    World Scientific Publshers, Singpore (2011);
    Low priced edition by Cambridge  University Press

    Errata to the above book will also appear in this tree hierarchy.

     

    kapoor's picture 22-08-17 13:08:10 n

    Complex Variables --- Principles and Problem Sessions === SOLUTIONS and ERRATA

    Node id: 2193curated_content

    It is proposed to post solutions to almost all the problem session in the book here. At present  solutions to  all most all Problem Sessions of Chapter 7, Contour Integration, has been completed. The solutions to problems in other chapters is being taken up.
    At  present solutions to problems in Chapter 3. "Function with Branch Point Singularity"
    is Being Uploaded.

    Errata is being compiled and will be uploaded in this book hierarchy.
    Click to see what is available.

    I take this opportunity to thank my friend and colleague, Prof. T. Amarnath, from School of Mathematics, University of Hyderabad for his kind words of appreciation and for recommending  the book to National Board of Higher Mathematics for inclusion in  scheme of distribution of mathematics books to Universities and Institutes in India.

    kapoor's picture 20-02-08 16:02:37 n

    Complex Variables --- Mostly contour integration

    Node id: 3032page

    The problem sessions included here are in addition to those in my book on complex variables.

    At present most problem sets are on method of contour integration for improper integrals.


    kapoor's picture 22-08-17 12:08:16 n

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