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• Module I :: Classical Field Theory
• I-1 Overview of Module-I
•  I-2 Let's Just Talk --- With as few equations as possible
• I-2.1 Talk:: What is a classical field?
• I-2.2 Talk:: Why reinterpret QM equations as classical equations
• I-2.3 Talk:: How to do classical mechanics of fields?
• I-3 Chalk Talks --- Tighten Your Belts 
• I-3.1 Chalk Talk:: Functional Derivative;
• I-3.2 Chalk Talk:: Action principle; Euler Lagrange formalism
• I-3.3 Chalk Talk:: Hamiltonian Formulation and Poisson Brackets
• I-3.4 Examples: Lagrangian and Hamiltonian for different systemsPoisson Bracket
•  I-4 Activities ---  Learn by Solving Problems
• I-4.1:: Submit a  Web-form --- What is a classical field?
• I-4.2 :: Submit a Web-Form --- Classical and Quantum Systems
• I-4.3::  Submit a Web-form --- Why Interpret QM equations as classical field equation?
• I-4.4 :: Tutorial --- Computing Functional Derivative
• I-4.5 :: Exercise ---- Functional Derivative; Lagrangian and Hamiltonian
• I-4.6::  Exercise ---- Hamiltonian EOM; Poisson brackets
• I-5:: EndNotes and References
• Module II:: Second Quantization of Schrodinger Field
• Module III:: Preparation From Quantum Mechanics-I:: Time Dependent Perturbation Theory
• Module IV:: Computation of Cross Sections and Life Times-I
• Module V:: Preparation from Relativistic Quantum Mechanics-I --- Klein Gordon Equation
• Module VI:: Quantization of  Klein Gordon Field
• Module VII:: Quantization of Electromagnetic Field
• Module VIII:: Preparation from Relativistic Quantum Mechanics-II  ----  Dirac Equation
• Module IX:: Quantization of Dirac equation
• Module-X:: Symmetries and Conservation Laws
• Module-XI:: S- Matrix, Schwinger Dyson Expansion, and Wick's Theorem
• Module-XII:: Feynman Diagrams and Feynman Rules
• Module- XIII::  Computation of  Processes --- Tree Diagrams
• Module-XIV:: Higher Order Calculation
• Module-XV:: Anomalous Magnetic Moment of Electron

This is a repository of QUESTIONS and PROBLEMS for Lectures in   Quantum  Field Theory  These are arranged according to topics in the subject.  Not sorted, or arranged, in any particular order within a topic.

The primary usage of these Questions is to use them as building blocks for other resources.

Suitable for teachers and content developers only.

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Rutherford formula\begin{eqnarray}
\sigma(\theta)
&=& \frac{1}{4} \left( \frac{k}{2E} \right)^{2} \frac{1}{\sin^{4}
\left(\frac{\theta}{2} \right)}
\end{eqnarray}for Coulomb scattering is derived in classical echanics.

It is shown that the total cross section from a hard sphere of radius \(R\) is \(\pi R^2\)

For scattering of particles, we explain which area is scattering cross section.

Summary Box

NO TOC here

Quantum Mechanics Lecture Notes -16 HOME PAGE
Spherically Symmetric Potential Problems

• General Properties of Spherically Symmetric Potentials
• Angular Momentum in Coordinate Representtaion
• Solution of Radial Equation
• Hyderogen Atom Energy Levels

$\newcommand{\dd}[2][]{\frac{d #1}{d #2}};\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}};$
We discuss an example of particle in two dimensions in  a potential independent of \(\theta\). By working in plane polar coordinates, we show how solution of  equations of motion   can be reduced to quadratures.