This course will provide the basic grounding in Quantum Mechanics for the undergraduate students. Topics to be covered in this course are (i) Fundamental concept (Hilbert space, Bra, Ket vectors, Operators, uncertainty relations, Wave functions), (ii) Quantum Dynamics (Time evolution of wave function, the Schrodinger vs Heisenberg picture, SHO), (iii) Angular Momemtum (Rotations and angular momentum commutations relation, spin 1/2 system, eigen values and eigenstates of angular momentum, orbital angular momemtum, angular momentum addition), (iv) Symmetry in quantum mechanics (symmetries, conservation laws and degeneracies, discrete symmetries etc), (v) Time-Independent perturbation theory, non-degenerate and degenerate cases, Stark effect and Zeeman effect. (vi) Variational principle and its application.
This
course aims to introduce the basic concepts of General Theory of Relativity and it's application in Cosmology i.e. to know the
behavior of the universe at large scale. After reviewing basic concepts
of special relativity (in 4 vector formalism), the notion of tensor,
covariant derivative, geodesics, curvature tensor, Ricci tensor, Ricci
scalar, Einstein tensor and hence the Einstein equations will be
derived. The Schwarzschild black hole solution of the Einstein equation
will be discussed, which will be followed by Physics near the massive
objects. The FRW cosmology will be discussed at a length and finally
inflationary cosmology will be introduced in brief.