Coherent States and Applications in Mathematical Physics

The standard coherent states of quantum mechanics.- The Weyl-Heisenberg group and the coherent states of arbitrary profile.- The coherent states of the Harmonic Oscillator.- From Schrödinger to Fock-Bargmann representation.-  Weyl quantization and coherent states: Classical and Quantum observables.- Wigner function.- Coherent states and operator norm estimates.- Product rule and applications.- Husimi functions, frequency sets and propagation.- The Wick and anti-Wick quantization.- The generalized coherent states in the sense of Perelomov.- The SU(1,1) coherent states: Definition and properties.- The squeezed states.- The SU(2) coherent states.- The quantum quadratic Hamiltonians: The propagator of quadratic quantum Hamiltonians.- The metaplectic transformations.- The propagation of coherent states.- Representation of the Weyl symbols of the metaplectic operators.- The semiclassical evolution of coherent states.- The van Vleck and Hermann-Kluk approximations.- The semiclassical Gutzwiller trace formula using coherent states decomposition.- The hydrogen atom coherent states: Definition and properties.- The localization around Kepler orbits.- The quantum singular oscillator: The two-body case.- The N-body case.