Selected Topics in Mathematical Physics (V. Balakrishnan, IIT Madras): Lecture 24

Selected Topics in Mathematical Physics

Selected Topics in Mathematical Physics. Instructor: Professor V. Balakrishnan, Department of Physics, IIT Madras. A basic course in mathematical methods used in physics. Analytic functions of a complex variable. Calculus of residues, Linear response; dispersion relations. Analytic continuation and the gamma function. Mobius transformations. Multivalued functions; integral representations. Laplace transforms. Fourier transforms. Fundamental Green function for the Laplacian operator. The diffusion equation. Green function for the Helmholtz operator; nonrelativistic scattering. The wave equation. The rotation group and all that. (from nptel.ac.in)

Lecture 24 - Fundamental Green Function for Δ² (Part II)

Coulomb potential in d dimensions. Ultraspherical coordinates. A divergence problem. Dimensional regularization. Direct derivation using Gauss' Theorem. The Coulomb potential in d = 2 dimensions.

Go to the Course Home or watch other lectures:

Lecture 01 - Analytic Functions of a Complex Variable (Part I)

Lecture 02 - Analytic Functions of a Complex Variable (Part II)

Lecture 03 - Calculus of Residues (Part I)

Lecture 04 - Calculus of Residues (Part II)

Lecture 05 - Calculus of Residues (Part III)

Lecture 06 - Calculus of Residues (Part IV)

Lecture 07 - Linear Response; Dispersion Relations (Part I)

Lecture 08 - Linear Response; Dispersion Relations (Part II)

Lecture 09 - Analytic Continuation and the Gamma Function (Part I)

Lecture 10 - Analytic Continuation and the Gamma Function (Part II)

Lecture 11 - Mobius Transformations (Part I)