Quantum Mechanics (a selfstudy course)
Textbook:
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.
Announcements:
This course will be run on the Brightspace platform. All announcements, assignments, etc. will be posted there.
Syllabus:
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 observablesclassification 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); BakerHausdorff 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 timedependent Schrödinger equation for a conservative system; solution of a timedependent Schrödinger equation for a twostate system in a harmonic field; operator method for simple harmonic oscillator; nondegenerate timeindependent perturbation theory.
Twostate systems (spin1/2, ammonia molecule, benzene molecule, H_{2}^{+}ion). SternGerlach experiment as a prototype for wavefunction collapse. Using symmetries to determine stationary states. Tentative: time dependence of a spin1/2 in a uniform magnetic field. EPR paradox and Bell's inequalities.
Course Policies:
 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.
Marking scheme:
10 Assignments (50%), Presentation (20%), Final examination (30%)
