Reports of the APT Workshop Series in Theoretical Physics

By G. Harikrishnan

Date of Report: 9 Jan 2015

Introduction   

            The profile of physics teachers of arts and science colleges in Govt., aided and unaided sectors has been in the process of a change over for the last decade and within the next few years it would be exclusively composed of young generation. They are keen on learning the subject in depth, acquiring new teaching skills and adapting themselves to the new era with equal emphasis on teaching and research. It is to address the needs of this young generation of physics teachers and equip them attain mastery in their subject matter and vocation that Academy of Physics Teachers (APT) has envisioned the Workshop Series in Theoretical Physics. This series will span all the fundamental theoretical areas being taught at the PG level. There will be one weekend workshop (Saturday & Sunday) every alternate month, 3-day workshops during Christmas, Onam and summer holidays. All the resource persons collaborating in the realization of this series are adepts in both the understanding of the subject matter and the skill in transferring their knowledge to the audience. On each day of the workshop, there will be lecture sessions for the presentation of the topics and tutorial sessions for problem solving and discussions so that the participants would get sufficient opportunity to clear their doubts. The topics to be discussed in each workshop and the text books to be followed would be announced in advance and it would be advantageous to the participants if they come prepared by going through the relevant reading material. These workshops can play a crucial role in generating academic excellence among the young teachers. It is hoped that anyone interested in expanding one’s knowledge base in physics and fine tuning one’s teaching skills would be motivated to attend this series. The plan of different workshop series is in the following order : I. Mathematical Physics, II. Classical Mechanics, III. Quantum Mechanics, IV. Statistical Mechanics, V. Electrodynamics and VI. Solid State Physics.

Series I : Mathematical Physics

Workshop 1 : Complex Analysis

        Download Brochure S1-1

The workshop was inaugurated by Rev. Fr. Dr. Jose Thekkan C.M.I., Principal, Christ College, Irinjalakuda. Dr. Satyanarayana addressed the gathering pointing out the uniqueness and significance of this workshop series launched by APT. Prof.V P Anto, Head in charge of the Dept. of Physics presided over the function. Dr. Shaju K Y, Secretary of APT welcomed the gathering and G Harikrishnan, state coordinator of the workshop series, delivered the vote of thanks. There were 43 participants out of which 22 were resident participants. They had come together from different parts of the state and three of them were from Karnataka. The video recording of the classes were done on both days.

On the first day the classes started with the discussion on the motivation for the invention of complex numbers. It proceeded to stereographic projection and then on to analytic function. The alternate way of stating Cauchy-Reimann conditions, in the form of ∂f∂z∗=0∂f∂z∗=0, sparked some interesting discussions.The logical progression from Cauchy integral theorem to Cauchy’s integral formula and finally to the definition of the derivative of an analytic function was systematically established. Taylor and Laurent series expansions were discussed in detail. Lecture sessions on the first day ended with the classification of different types of singularities and the calculation of residue. During the tutorial sessions, many standard problems that are frequently being asked in the PhD entrance examinations and interviews, like finding the real and imaginary parts of ii√ii, were analyzed. Many of the problems were directly connected to different physical phenomena. The second day began with the exposition of analytic continuation and then contour integration. Five major types of contour integration were taken up one by one and analyzed at length. Multivalued functions, branch points and branch cuts were then discussed. Green’s function method of solving the inhomogeneous differential equation was illustrated by the problem of forced oscillator and quantum theory of scattering. In both cases, the evaluation of the Green’s function involved contour integration. In the tutorial sessions, examples involving multivalued functions were considered.

            The participants were supplied with the LaTex and pdf versions of the notes on Complex Analysis prepared by Dr. P. D. Shaju, Dept. of Physics, Christ college, Irinjalakuda.