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12731 Advanced Quantum Mechanics - M. ADVANCED PHYSICST, SPE. ASTROPHYSICS


Center
Student Information Service-Master
Departament
Theoretical Physics
Lecturers in charge
Sin datos cargados
Met. Docent
A final written exam in two parts: theory and problems. 0 to 10 points. During the course the students will be given practical problems to solve, which will be considered in the final qualification.
Met. Avaluació
- -
Bibliografia
J. J. Sakurai. "Modern Quantum Mechanics"
Addison - Wesley Publising Company, (1985).
A. Galindo y P. Pascual. "Mecanica Cuantica".Vol. I, II
F. Yndurain. "Mecanica Cuantica". AlianzaEditorial (1988).
A. Messiah. "Quantum Mechanics". Vol. I y II.North - Holland
R. H. Landau. "Quantum Mechanics II". JohnWiley & Sons
Continguts
1.ROTATIONS
Angular moment as generator of rotations. Matrix representation of rotation operators. Spin 1/2. SU(2,C) and SO(3,R). Construction of irreducible representations. Explicit forms (Euler angles). States of Helicity.

2.SYMMETRIES
Introduction. Symmetry transformations. Theorem of Wigner. Transformation of operators. Symmetry groups. Spatial translations. Rotations. Parity. Temporary inversion. Phases and temporary inversion. Invariance and Laws of Conservation.Hamiltonian invariance (linear case). Laws of Conservation. Applications. Invariance under temporary inversion. Electric dipolar moment.

3.PARTICLE IN AN ELECTROMAGNETIC FIELD
Introduction. Schr÷dinger equation and gauge invariance. ˘ Spin particle in an electromagnetic field. Applications. Particle in a uniform magnetostatic field. Aharanov-Bohm effect.

4.FORMALISM OF IDENTICAL PARTICLES
Wave function symmetrization. States of identical particles without mutual interaction. Creation and annihilation operators.

5.QUANTUM THEORY OF THE RADIATION
Quantizing of the electromagnetic field. Canonical Quantizing. Towards the continuous. Photon states. Matter-radiation interaction. Electric dipolar transition.

6. PATH INTEGRALS
Propagators in Quantum Mechanics. Propagator as a transition amplitude. Feynman formulation of the Quantum Mechanics