On Second Order Linear Ordinary Differential Equations and its Applications in Physics

Sundaram, Sriram (2016) On Second Order Linear Ordinary Differential Equations and its Applications in Physics. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Sriram S (11MS021)) Sriram_S_11MS021_MSthesis.pdf - Submitted Version Restricted to Repository staff only Download (414kB)

Abstract

We study, second order linear ordinary differential equations and its several applications in Physics. In the first part, coherence properties of sunlight is investigated in the light of differential equation using small angle approximation. It is shown that the observed far field behaviour of sunlight on Earth’s surface, located in the near field region, is due to the small angular width it subtends at the center of the Sun. In second part, Supersymmetric Quantum Mechanics (SUSY-QM) inspired factorization of second order linear ordinary differential equations is dealt with. Heun class of operators are taken as examples to illustrate the proposed method. Such a factorization and corresponding solutions can be found for a set of parametric conditions. Factorization of Biconfluent Heun equation is revisited with oscillator algebra, mapping the biconfluent Heun functions onto Hermite polynomials and its corresponding physical applications are highlighted.

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