Course Details

Subject {L-T-P / C} : PH3006 : Basic Mathematical Physics { 3-0-0 / 3}

Subject Nature : Theory

Coordinator : Prof. Sanjoy Datta

Syllabus

Curvilinear coordinates: transformation of coordinates, orthogonal curvilinear coordinates. Unit vectors, arc length, volume elements, gradient, divergence, curl and Laplacian in curvilinear systems. Special orthogonal coordinate systems cylindrical, spherical coordinate systems. Ordinary differential equations (ODE): linear second order differential equations with variable coefficients, power series method and Frobenius method of solving differential equations. Special functions: Bessel’s function, Legendre function, Hermite function, Laguerre function and their properties othogonality, recurrence relations, generating functions. Generalized functions: step function, Dirac delta function-definition, representation of Dirac delta function in terms of conventional functions, relation between Dirac delta and step function, Fourier representation of the delta function, properties of delta function. Partial differential equations (PDEs): first order PDE and its solutions, different classes of second order PDEs and boundary conditions, separation of variables and Laplace equation in cartesian and spherical polar coordinate systems, solution of homogeneous Helmholtz equation with constant coefficient in cartesian, circular cylindrical and spherical polar coordinate systems, inhomogeneous self-adjoint linear ordinary differential operator and Green function, eigenfucntion expansion of Green function. solving Poisson’s equation by Green function method. Special matrices: real, symmetric and hermitian matrices, number of independent parameters, independent matrices and linear combinations, orthogonal matrix, independent elements of orthogonal matrix, unitary matrix, independent elements of a unitary matrix, 2x2 special unitary matrix, orthogonal and unitary transformations, transformation of vectors and matrices, direct sum and direct product of matrices.

Course Objectives

Course Outcomes

After completion of the course a student will have the strong mathematical base and shall find it easier to follow upcoming theoretical courses, such as Electricity and Magnetism, Elements of Quantum Mechanics, Electrodynamics, Quantum Mechanics – I, Quantum Mechanics – II.

Essential Reading

Supplementary Reading