momentum and symmetries in quantum mechanics from group theory
viewpoint; time-independent and time-dependent perturbation theory;
path integral formulation; scattering theory; identical particles;
Possible principal texts:
Diu and Laloe, Quantum Mechanics
- 2 vols. (Wiley-Interscience)
Principles of Quantum Mechanics
Müller, Quantum Mechanics: Symmetries
Other texts to consider:
Sakurai, Modern Quantum Mechanics
The prerequisite is
one semester of a Quantum Mechanics
course at the level of R. Shankar's textbook.
In Duke Physics, there is an
undergraduate "Quantum Mechanics I" course (PHY 211), with the synopsis:
Experimental foundation of quantum mechanics; wave-particle duality; the single-particle Schrodinger equation and the physical meaning of the wave function; methods for studying the single-particle Schrodinger equation; analytical solutions of the harmonic oscillator and hydrogen atom and experimental tests of these solutions; angular momentum and spin systems; and finally the many-particle Schrodinger equation and consequences of identical particles existing in nature.
“real” hydrogen atom.
particles, exchange interaction, helium atom.
states, Slater determinant, Hartree-Fock approximation.
method: hydrogen molecule, chemical binding.
potential, Bloch waves, band structure.
perturbation theory, Fermi’s Golden Rule.
to two-state system (e.g., spin rotations, NMR).
two-state systems: neutral kaons or neutrino oscillations.
symmetries, Noether’s theorem, rotation group SO(3).
of angular momenta,
operators, Wigner-Eckart theorem.
and its relationship to SO(3), isospin (weak & strong).
integral formulation of QM: Principles, free particle,
semiclassical limit, particle on a circle, Berry’s phase.
theory: cross section, S-matrix, T-matrix, unitarity,
partial waves, optical theorem.
special topics: quantum information theory, renormalization group,
There is a
2009 Duke University