PHYS 404 Mathematical Physics III (BSc)

This heavy and intensive course mainly deals with mathematical methods in physics. The course covers special functions of integral form and their applications in physics. This includes gamma and beta functions. Additionally, it covers special functions of derivative form and their applications in physics. This part includes the following: (1) Legendre special functions and their application in electrostatics It also covers, associated Legendre functions and applications in magnetostatics and nuclear physics, spherical harmonics and applications in quantum mechanics (2) Bessel functions of all types and their applications in the wave mechanics, electrodynamics and quantum mechanics (3) Laguerre and Associated Laguerre functions and their applications in quantum mechanics (4) Hermite functions and their applications in solving the quantum harmonic oscillator. The integral transforms are also covered in this course: (1) Fourier series, transformations and integrals and their applications in the physics of waves (wave equation), (2) Laplace transformations and their application in the physics of waves, heat transfer (heat equation)

Basic reference: Mathematical Methods for Physicists, G. B. Arfken, H. J. Weber, and F. E. Harris