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
