Quantum Mechanics
Textbook:
There is no required text for this course. The library has many texts on this subject and I leave it to students to pick their favorite one. I don't follow closely any particular text (perhaps Sakurai's Modern Quantum Mechanics is closest in spirit to my lecture notes) and I view the textbook as a complement to the lecture material. A copy of my lecture notes will be available to students in the main office (MC B210).
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.
Most of the material is illustrated in the case of a twostate system (spin1/2, ammonia molecule, benzene molecule, H_{2}^{+}ion). SternGerlach experiment is used as a prototype for filtration measurement. How symmetries are used to simplify the solution of the eigenvalue problem of a Hamiltonian is illustrated by solving the eigenvalue problem of an electron moving in a onedimensional lattice via the nearest neighbor hopping (; the case which also includes the second nearest neighbor hopping or the twodimensional case are given as homework. The time dependence of a spin1/2 in a uniform magnetic field is examined in detail (the time dependence of other twostate systems is assigned as homework). The basic principles of the Electron Spin Resonance (ESR) and Nuclear Magnetic Resonance (NMR).
Course Policies:
 Penalty for Late Assignments: 10% deduction per day.
 A student must achieve 50% on the final exam to pass the course.
 Note that the last day to withdraw without academic penalty is Tuesday, Nov. 6, 2018.
Marking scheme:
10 assignments (45%), 1 midterm test (10%) on Tuesday, October 23, final exam (45%)
