Methods of Theoretical Physics 2

Instructor

Benjamin Svetitsky

Email :bqs@julian.tau.ac.il

Academic Year, Semesters

2nd semester, 2017-18

Number of Hours/ Credits

2h lec. + 1h ex.

Mandatory/Elective

Required course

Prerequisites

Methods of Theoretical Physics 1

Year in program & how often given, if relevant

2nd year (physics)/
3rd year (physics+EE)

Syllabus

Course overview – short abstract

Special functions; asymptotic analysis; singular perturbations of differential equations; introduction to group theory

Learning outcomes – short description

Assessment: coursework and grade structure

Assignments – 10%
Final exams – 90%

Week-by-week content, assignments and reading

Week 1:  Gamma function; digamma, beta functions.

Week 2:  Incomplete gamma function and related functions. Bessel functions: generating function, recurrence relations, power series, Bessel equation.

Week 3:  Bessel functions: integral representations.  Separation of Helmholtz equation in cylindrical coordinates; Fourier-Bessel series.

Week 4: Neumann functions, Hankel functions.

Week 5: Modified Bessel functions, spherical Bessel functions.  Contour integral representations and asymptotic forms.

Week 6: Hermite polynomials.

Week 7: Laguerre, associated Laguerre, and Chebyshev polynomials.  Asymptotic series.

Week 8: Asymptotic approximations to integrals: integration by parts, Laplace’s method, Watson’s Lemma.

Week 9: General Laplace integrals.  Stirling series for the gamma function. Stationary phase method and the Riemann-Lebesgue lemma.

Week 10: Steepest descent.

Week 11:  Singular perturbations of differential equations: boundary layer theory, WKB.

Week 12: Introduction to group theory.  Matrix groups.

Week 13: Lie groups and Lie algebras

Required texts

Mathematical Methods for Physicists, G. B. Arfken and H. J. Weber

Advanced Mathematical Methods for Scientists and Engineers, C. M. Bender and S. Orszag