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Title+Summary	Name	Date
CM-Mod10 Canonical Transformations Node id: 1955page	kapoor	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	20-02-08 16:02:01	n
CM02 Lagrangian Form of Dynamics (ProbSets) Node id: 901page	kapoor	19-12-28 03:12:44	n
CM05 Solution of Equations of Motion (ProbSets) Node id: 903page	kapoor	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	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 Basic Definition A simple example 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	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 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 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	21-12-02 10:12:17	n
Collection of Video and Animation Links for Class Room Node id: 4173collection Classical Mechanics Small Oscillations Coupled Pendulum Double Pendulum	kapoor	21-05-20 04:05:31	n
Comments embedded in array of equations Node id: 253page	kapoor	19-12-28 03:12:19
Commutator Node id: 283page	kapoor	19-12-28 03:12:19
Complete Orthonormal Sets Node id: 812page	kapoor	19-12-28 03:12:51	n
Complex Variables Node id: 5619forum	kapoor	22-08-07 13:08:52
Complex Variables Node id: 2989page	kapoor	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	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	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	22-08-17 12:08:16	n
Complex Variables -- Problem Sets Node id: 2949page	kapoor	20-03-08 16:03:30	n
Complex Variables :: Contour Integration Node id: 2960page Here we list a sample of kinds of integrals that can be evaluated by the method of contour integration. Each problem requires a different method. A link is provided where you can find more examples.	kapoor	22-08-17 13:08:40	n
Complex-Variables-Home [CV-HOME] [LNK] Node id: 3488collection Complex Variables --- Principles and Problem Sessions SOLUTIONS and ERRATA Chapter-1 Complex Numbers 1.1 Polar Form of Complex Numbers Q1-Q5 1.2 Curves in Complex Plane Q1-Q3 1.2 Curves in Complex Plane Q4-Q7 Chapter-2 :: Elementary Functions and Differentiation 2.1 Exercise De Moivre's Theorem 2.2 Real and Imaginary Parts 2.4 Exercise Solutions of Equations (Q1-Q2) 2.4 Exercise Solutions of Equations (Q3-Q5) \(\S\S\) 2.6 Tutorial Roots of a complex number; and \(\S\S\) 2.7 Quiz : Roots of Unity. Chapter 3 :: Functions with branch cut singularity 3..1 Questions ----------- Branch Point 3..2 Tutorial ---The square root branch cut 3.3 Exercise Branch cut for 3.4 Quiz Discontinuity and branch cut 3.5 Exercise The Logarithmic function 3.6 Discontinuity across the branch cut 3.8 Mixed Bag Multivalued Functions 3.8 Mixed Bag Q[1] 3.8 Mixed Bag Q[2] 3.8 Mixed Bag Q[3] 3.8 Mixed Bag Q[4] 3.8 Mixed Bag Q[5] 3.8 Mixed Bag Q[7] 3.8 Mixed Bag Q[8] 3.8 Mixed Bag Q[11] 3.8 Mixed Bag Q[12] 3.8 Mixed Bag Q[13] Chapter 4 :: Integration in Complex Plane \(\S\S\) 4.1 Questions Range of Parameters In Improper Integrals Q[1] \(\int_{-\infty}^\infty \frac{}dx{(x^4+1)^c} \), Q[2], Q[3] Q[4] \(\\int_0^\infty \frac{x^c}{\sinh x} Q[5] \(\int_0^\infty \frac{e^{cx}}{\cosh^2x}\), Q[7] \(\int_{-\infty}^\infty \frac{x^{2n+1}{(x^2+1)}\); Q[8]; Q[9] Q[10] \(\int_0^\infty\frac{x^c(e^{ax}-1)}{(x^3+2)^c} \) Q[11] \( \int_0^\infty \frac{x^2}{e^x-1}; Q[12} ; Q{13]; Q[14] \) \(\S\S\) 4.2 Tutorial Computing Line Integrals in Complex Plane Q[1] \(\int_{x_1}^{x_2} \exp(\lambda x) dx = \frac{1}{\lambda}\[\exp(\lambda x_2) -\exp(\lambda x_2) \]\) Q[3] \(\int_\Gamma z^2 dz\) \(\S\S\) 4.3 Exercise Evaluation of Line Integrals \(\S\S\) 4.4 Questions Deformation of Contours \(\S\S\) 4.5 Exercise Deformation of Contours \(\S\S\) 4.6 Exercise Cauchy Theorem \(\S\S\) 4.7 Tutorial Shift of Real Integration Parameter by a Complex Number Q[1] Prove that \(\int_0^\infty exp(-px^2) \cos(2bx)\, dx= \frac{1}{2}\sqrt{\frac{\pi}{p}} \exp(-b^2/p), p>0 \) Q[2] Prove that \(\int_0^\infty e^{-px^2} \sin(ax) \sin(bx) = \frac{1}{4} \left\{\exp\Big(\frac{(a-b)^2}{4p}\Big)- \exp\Big( -\frac{-(a+b)^2}{4p}\Big) \right\}\) \(\S\S\) 4.8 Tutorial Scaling of a Real Integration Variable by a Complex Number Q[1] Prove \(\int_0^\infty e^{ipx^2}\, dx = \frac{1}{2} e^{i\pi/4}\sqrt{\frac{\pi}{p}} \) \(\S\S\) 4.9 Exercise Shift and Scaling by a Complex Number Q[1] \(\int_0^\infty e^{-q^2x^2} \sin^2 ax\, dx\) Q[2] \(\int_0^\infty e^{-q^2x^2}{\,\sin(px+c)\,\choose\, \cos (px+c)\,}\, dx \) Q[3] \( \int_0^\infty x e^{-q^2x^2} \sin ax \, dx\) Q[4] \( \int_0^\infty x^2 e^{-q^2x^2} \cos ax\, dx\) Q[5] \(\int_0^\infty x^3 e^(-q^2x^2) \sin ax \, dx \) Q[6] \(\int xe^{-px} \cos (2x^2+px) \, dx\) Q[7] \(\int xe^{-px} \cos (2x^2-px) \, dx\) Q[8] \(\int_0^\infty e^{-px} \big[ \sin(2x^2+px)+\cos(\cos (2x^2 +px) ) \big]\, dx\) Q[9] \( \int_0^\infty e^{-px} \big[ \sin(2x^2-px)-\cos(\cos (2x^2 -px) ) \big]\, dx\) Q[10] \(\int_0^\infty xe^{-\beta x} \sin ax^2 \sin\beta x\, dx\) Q[11] \(\int_0^\infty \cos ax^2 \cos 2bx, dx\) Q[12] \(\int_0^\infty (\cos ax +\sin ax) \sin(bx)^2\, dx\) Q[13] \(\int_0^\infty \sin ax^2 \sin 2bx \sin 2cx\, dx\) Q[14] \(\int_0^\infty x \sin ax^2 \sin2bx \,dx\) Q[15] \(\int_0^\infty \sin ax^2 \cos bx^2\, dx\) Q[16] \(\int_0^\infty (\sin^2 ax^2 -\sin^2bx^2)\, dx\) Q[17] \(\int_0^\infty \big(\sin (a-x^2) + \cos(a-x^2) \big)\, dx\) \(\S\S\) 4.10 Exercise Rotation of Contour \(\S\S\) 4.11 Mixed Bag Chapter 5 :: Cauchy Integral Formula \(\S\S\) 5.2 5.2 Q 1-Q12 \(\S\S\) 5.3 5.3 Q3 5.3 Q4 Q8 5.5 Q1-Q2 \(\S\S\) 5.5 5.5 Q 3-Q4 \(\S\S\) 5.4 :: Taylor Series Representation 5.4 Q[1] 5.4 Q[2] 5.4 Q[3](a)-(b) 5.4 Q[3](c)-(d) 5.4 Q[3](e)-(g) 5.4 Q[4] 5.4 Q[5] \(\S\S\) 5.8 :: Laurent Expansion of \(f(z)\) in powers of \((z-z_0) 5.8 Q[1] \(f(z) = (z^2+3z+5) e^{1/z}, z_0=0.\) 5.8 Q[2] \(f(z) = \frac{\text{cosh}\, z}{z(z^4+1)}, z_0=0.]\) 5.8 Q[3] \(f(z) = z^2 \sin(1/(1-z)), z_0=1.\) 5.8 Q[4] \(f(z) = \frac{z}{\text{cosh}\, z -1}, z_0=0. \) 5.8 Q[5] \(f(z) = \cot z , z_0=0. \) 5.8 Q[6] \(f(z) = \text{cosech}\, z, z_0=0. \) 5.8 Q[7] \(f(z) = \text{sec } z, z_0=\pi/2.\) 5.8 Q[8] \(f(z)=\frac{z+3}{\sin z^2}, z_0=0.\) 5.8 Q[9]\(f(z)=\frac{z}{\sin^3 z}, z_0=n\pi.\) 5.8 Q[10]\(f(z)= \frac{z}{\sin\pi z^2}, z_0=1.\) 5.8 Q[11]\(f(z)= \frac{1}{(\exp(z)-1)}, z_0=0.\) 5.8 Q[12] \(\frac{1}{(\exp(z)+1)^2)}, z_0=i\pi\) 5.8 Q[13] Prove \(\exp(t(z+1/z))= \sum_{-\infty}^\infty z^n J_n(t).\) 5.8 Q[14]\(f(z) = \sin(\pi/z), z_0=1.\) Chapter 6 :: The Residue Theorem \(\S\S\) 6.10 Integrals Using the Residue at Infinity Some general, common remarks 6.10 Q[1] \(\oint \sqrt{(z-a)(z-b)}\, dz= -(\pi i/4)(a-b)^2\) 6.10 Q[2] \(\oint \sqrt{\frac{z-a}{z-b}\, dz} = -(\pi i/2)(a-b)\) 6.10 Q[3] \(\oint \frac{z}{\sqrt{z-a}{z-b}}\, dz = \pi i (a+b)\) 6.10 Q[5] \(\int_0^1 \frac{x^{1-p}(1-x)^p}{(1+x)^3}\, dx\) 6.10 Q[6] \(\int_0^1\frac{x^{1-p}(1-x)^p}{1+x^2}\, dx\) 6.10 Q[7] \(\int_0^1 \frac{x^{1-p}(1-x)^p}{(1+x^2)^2}\, dx\) 6.10 Q[8] \(\int_0^1 \frac{1}{(1+x)^3(x^2(1-x))^{1/3}}\, dx\) 6.10 Q[9] \(\int \frac{x^{2n}}{(1+x^2)\sqrt{1-x^2}}\, dx\) 6.10 Q[10] \(\int_0^1 \frac{x^{2n}}{(x(1-x^2))^{1/3}}\) 6.10 Q[11] \(\int_0^1 \frac{1}{(1-x^n)^{1/n}}\, dx\) Chapter 7 :: Contour Integration \(\S\S\) 7.1 Tutorial Integrals of Rational Function 7.1 Q[1] 7.1 Q[2] \(\S\S\) 7.2 7,2. Q[1] 7.2 Q[2} \(\S\S\) 7.3 Exercise 7.3 Q[1] \(\int_0^\infty\frac{dx}{(x^2+p^2)^2} \) 7.3 Q[2] \(\int_0^\infty \frac{x\, dx}{x^4+1}\) 7.3 Q[4]\(\int_{-\infty}^\infty \frac{dx}{(x^2+x+1)^2}\) 7.3 Q[5] \(\int_{-\infty}^{\infty} \frac{(x^2+2) dx}{(x^4+10x^2+9)}\) 7.3 Q[6] \(\int_0^\infty \frac{(x-2)dx}{(x^4+10x^2+9)}\) 7.3 Q[7] \(\int_0^\infty \frac{x^2\, dx}{x^6+1}\) 7.3 Q[8] \(\int_0^\infty \frac{dx}{(x^2+p^2)(x^2+q^2)}\) 7.3 Q[10] \(\int_0^\infty \frac{x^2\, dx}{x^{2N+1}+1}\) 7.3 Q[11] \(\int_0^\infty \frac{x^4\, dx}{x^{2N}+1}\) 7.3 Q[12] \(\int_0^\infty \frac{dx}{x^N+1}\) 7.3 Q[13] \(\int_0^\infty \frac{x^{2N}\,dx}{x^{2M}+1}\)7.3 Q[14] \(\int_0^\infty \frac{dx}{(p+qx^2)^N}\) \(\S\S\) 7.4 Exercise ---Integrals of \(\sin x / \cos x\) with rational functions. 7.4 Q[1] 7.4 Q[2] \(\int \frac{\cos p x\, dx}{(x^2+1)^2}\) 7.4 Q[3] 7.4 Q[4] 7.4 Q[5] 7.4 Q[6] 7.4 Q[7] 7.4 Q[9] 7.4 Q[10] 7.4 Q[11] 7.4 Q[12] \(\S\S\) 7.5 Tutorial Integration Around a Branch Cut \(\S\S\) 7.6 Integration around a branch cut 7.6 Q[1] 7.6 Q[2] 7.6 Q[3] 7.6 Q[4] 7.6 Q[5] 7.6 Q[7] 7.6 Q[8] 7.6 Q[9] 7.6 Q[11] 7.6 Q[12] 7.6 Q[13] 7.6 Q[14] \(\S\S\) 7.7 Integral of Type \(\int 7.7 Q[1] 7.7 Q[2] 7.7 Q[3] 7.7 Q[4]-[6] 7.7 Q[7] 7.7 Q[8] 7.7 Q[9] 7.7 Q[11] 7.7 Q[12] \(\S\S\) 7.8 Hyperbolic Functions \(\S\S\)7.9 Exercise ----- Exponential and Hyperbolic Functions 7.9 Q[1] 7.9 Q[3] 7.9 Q[4] 7.9 Q[5] 7.9 Q[6] 7.9 Q[7]-[10] 7.9 Q[11] 9 Q[12] 7.9 Q[13] 7.9 Q[14] \(\S\S\) 7.10 Tutorial Principal Value Integrals 7.10 Q[1] 7.10 Q[2] \(\S\S\) 7.11 Exercise Integrals Requiring Indented Contours 7.11 Q[1] 7.11 Q[2] 7.11 Q[3] 7.11 Q[4] 7.11 Q[5] 7.11 Q[6] 7.11 Q[7] 7.11 Q[8] 7.11 Q[9] 7.11 Q[10] \(\S\S\) 7.12 Series Summation and Expansion 7.12 Q[1] 7,12 Q[5] \(\S\S\) 7.13 What you see is not what you get 7.13 Q[1] 7.13 Q[2] 7.13 Q[3] 7.13 Q[4] 7.13 Q[5] 7.13 Q[6] 7.13 Q[7] 7.13 Q[8] 7.13 Q[9] 7.13 Q[10] 7.13 Q [11] 7.13 Q[12] \(\S\S\) 7.14 Integrals from Statistical Mechanics 7.14 Q[1] 7.14 Q[2] 7.14 Q[3] 7.14 Q[4] 7.14 Q[5] \(\S\S\) 7.15 Alternate Routes Improper Integrals 7.15 Q[1] 7.15 Q[2] 7.15 Q[4] \(\S\S\)7.16 Killing Two Birds with One Stone 7.16 Q1] 7.16 Q[2] 7.16 Q[3] 71.6 Q[4] \(\S\S\) 7.17 7.17 Q[1] 7.17 Q[6] 7.17 Q[7] 7.17 Q[8] \(\S\S\) 7.18 Mixed Bag : Improper Integrals Errata for Complex Variables ----Principles and Problem Sessions Errata--Part-I :: Chapters 1-2 Errata -- Part-I:: Chapter 4 Integration in Complex Plane Errata -- Part-I :: Chapter 5 Cauchy's Integral Formula Errata -- Part-I :: Chapter 6 Residue Theorem Errata -- Part-II :: \(\S\S\) 1.9Mixed Bag Errata -- Part-II ::\(\S\S\) 3.6Exercise Discontinuity across the branch cut	kapoor	22-08-26 00:08:04	n
Computing Cross section Node id: 3544page Question Consider a system of two real scalar fields \(\phi_1, \phi_2\) described by the Lagrangian density \begin{equation} \Lsc = \frac{1}{2} \partial_\mu \phi_i \partial^\mu \phi_i - \frac{1}{2} m^2 \phi_i\phi_i -\frac{1}{4} \lambda (\phi_i\phi_i)^2. \end{equation} Compute the scattering cross section to the lowest order in \(\lambda\). Find the cross sections for the three processes \(\phi_1 + \phi_2 \longrightarrow \phi_1 +\phi_2\) \(\phi_1 + \phi_1 \longrightarrow \phi_1 +\phi_1\) \(\phi_1 + \phi_1 \longrightarrow \phi_2 +\phi_2\) Write your answers as a constant times \(\sigma_0\equiv \frac{\lambda^2}{64\pi s}\) where \(s\) is the total energy in the center of mass frame. Answer : a. \(4\sigma_0\) b. \(36 \sigma_0\) c. \(4 \sigma_0\) Hint : Find symmetry appropriate factor. Remark : Good question	kapoor	20-03-18 06:03:00	n

Browse & Filter

CM-Mod10 Canonical Transformations

CM-Mod11 :: Hamilton Jacobi Theory

CM02 Lagrangian Form of Dynamics (ProbSets)

CM05 Solution of Equations of Motion (ProbSets)

CM@HCU :: Tutorial I

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

Dirac Delta function

Green Function

Vectors and Tensors

Collection of Packs for Newbies

Quantum Field Theory

1

2

Quantum Mechanics

1

2

Collection of Video and Animation Links for Class Room

Classical Mechanics

Comments embedded in array of equations

Commutator

Complete Orthonormal Sets

Complex Variables

Complex Variables

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

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

Complex Variables --- Mostly contour integration

Complex Variables -- Problem Sets

Complex Variables :: Contour Integration

Complex-Variables-Home [CV-HOME] [LNK]

Chapter-1 Complex Numbers

Chapter-2 :: Elementary Functions and Differentiation

Chapter 3 :: Functions with branch cut singularity

Chapter 4 :: Integration in Complex Plane

Chapter 5 :: Cauchy Integral Formula

Chapter 6 :: The Residue Theorem

Chapter 7 :: Contour Integration

Errata for Complex Variables ----Principles and Problem Sessions

Computing Cross section

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