Quantum Mechanics I

Review of fundamental principles in quantum mechanics. General formulation of quantum mechanics, including Dirac's bra-ket notation and the harmonic oscillator. Angular momentum: spin, orbital angular momentum and addition of angular momenta. Identical particles: ideal Fermi gas and ideal Bose gas; atoms and solids. Variational methods. Perturbation theory.

Upon completion of this course, the student should:

i) master the central aspects of basic quantum mechanics: basic postulates and central theorems, eigenfunctions and eigenvalues, expansions in terms of eigenfunctions, stationary and non-stationary states, square-well potential, harmonic oscillator, the hydrogen atom,

ii) have learned how to use the Dirac formalism, and how to apply operator algebra to quantize angular momentum and the harmonic oscillator,

iii) be familiar with spin formalism and addition of angular momenta,

iv) comprehend the theory and the implications of identical particles, especially ideal Fermi and Bose gases,

v) understand the main concepts of perturbation theory.

In addition, the student should learn how computational physics can help solve and understand quantum-mechanical problems.

Lectures and compulsory exercises. Computational physics components may be included in the lectures and the homework assignments. The student's expected workload in the course is 225 hours.