Sri S. Ramasamy Naidu Memorial College, Sattur, Tamil Nadu, 17-31 March, 2025
Classical & Quantum Mechanics Topics: Formulation of classical mechanics, Hamilton's equations, Poisson brackets, States and observables in quantum mechanics, Hilbert space of states of a quantum system, Linear operators, Adjoint, (anti-)Hermitian and Unitary operators, Outer products of vectors and completeness relation, projection operators, Commutators of operators, Quantization: Heisenberg canonical commutation relations and Schrodinger representation, Hermiticity of position and momentum operators, Eigenvalue problem for hermitian operators, Spectral theorem for hermitian operators, Relation between wave function in position and momentum space, Measured value of observables in states and interpretation of expectation values, Collapse postulate, Projective measurements, Reproducibility of measurements, Simultaneous measurability of compatible observables, Heisenberg uncertainty principle and inequality, Density matrix of pure and mixed ensembles, Time evolution: Schrodinger equation, Separation of variables, stationary states, Time evolution operator and its Unitarity, Conserved probability density and current, Ehrenfest's theorem.
Probabiity Topics: Outcomes of an experiment, events, sample space, probabilities and combination of events, conditional probability and statistical independence, random variables: discrete and continuous, probability distributions, cumulative distribution, probability density, joint probability density, marginal distribution, statistical independence, expectation value, variance, moments, Bernoulli trials, Binomial distribution, Poisson distribution, Gaussian distribution.
Some brief lecture notes on Quanutum Mechanics are here.
Some brief lecture notes on Probability are here.