Topics: Formulation of classical mechanics, 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, Hermiticity of position and momentum operators, Expectation values, Commutators of operators, Eigenvalue problem for hermitian operators, Measured value of observables in states and interpretation of expectation values, Expectation value, Collapse postulate, Reproducibility of measurements, Simultaneous measurability of compatible observables, Heisenberg uncertainty principle and inequality, Relation between wave function in position and momentum space, Density matrix, Time evolution: Schrodinger equation, Separation of variables, stationary states, Conserved probability density and current, Ehrenfest's theorem.
Bishop Moore College, Mavelikara, Kerala, June 15 - July 1, 2023
Some brief lecture notes on Quanutum Mechanics are here.
Some exercises on quantum mechanics are here.