We will tentatively follow David Tong's lectures on quantum mechanics and topics in quantum mechanics. There are many other excellent books (Sakurai, Gasiorowicz, Griffiths) that can be useful references.

This course will be run on the Brightspace platform. All announcements, assignments, etc. will be posted there.

Postulates about (pure) states, observables, probabilities, change of state in a filtration measurement, quantization of a classical system and the time evolution of a quantum mechanical system.

Dirac's bra and ket notation; representation and transformation theory (coordinate and momentum representations as the important special cases); the eigenvalue problem and the spectral form of a Hermitian operator (observable); general Heisenberg's uncertainty relations; commuting observables and a complete set of commuting observables-classification of states in terms of the compatible eigenvalues of the observables from a complete set; solution of the eigenvalue problem for general angular momentum; analytic functions of operators (definition in terms of the power series expansions) and functions of Hermitian operators (definition in terms of a spectral form of a Hermitian operator); Baker-Hausdorff theorem and some other important operator identities; commutator algebra; symmetries; angular momentum as a generator of spatial rotations, momentum as a generator of spatial translations; position operator as a generator of boosts; Hamiltonian as a generator of translations in time; using symmetries in solving the eigenvalue problem of a Hamiltonian; stationary states and the solution of a time-dependent Schrödinger equation for a conservative system; solution of a time-dependent Schrödinger equation for a two-state system in a harmonic field; operator method for simple harmonic oscillator; nondegenerate time-independent perturbation theory.

Two-state systems (spin-1/2, ammonia molecule, benzene molecule, H₂⁺-ion). Stern-Gerlach experiment as a prototype for wavefunction collapse. Using symmetries to determine stationary states. Tentative: time dependence of a spin-1/2 in a uniform magnetic field. EPR paradox and Bell's inequalities.

• A student must achieve 50% on the final exam to pass the course.
• Note that the last day to withdraw without academic penalty is Monday, Nov. 5, 2024.

10 Assignments (50%), Presentation (20%), Final examination (30%)