DEPARTAMENTO DE FÍSICA

Quantum Mechanics II - F

Ano letivo: 2019-2020

Specification sheet

Specific details

course code | cycle os studies | academic semester | credits ECTS | teaching language |

1002863 | 1 | 2 | 6 | pt |

Learning goals

Understand the formalism of quantum mechanics. To know how to quantize a classical system. Understand the behavior of systems of identical particles. Master the use of principles of symmetry in Quantum Mechanics. To know how to calculate cross sections.

Generic skills: Competence in oral and written communication; Competence to solve problems; Competence in independent learning; Adaptability to new situations; Competence to investigate; Group work in competence; Competence in critical thinking; Competence to communicate with people who are not experts in the field;

Generic skills: Competence in oral and written communication; Competence to solve problems; Competence in independent learning; Adaptability to new situations; Competence to investigate; Group work in competence; Competence in critical thinking; Competence to communicate with people who are not experts in the field;

Syllabus

Systems of identical particles: the principle of indistinguishability. Exchange Operators. Exchange degeneracy and the postulate of symmetrization.

Symmetries in Quantum Mechanics: symmetry transformations and operators that represent symmetry transformations. Symmetry groups. Groups of continuous transformations: generators and the maximum set of operators that commute. The decomposition of the Hilbert space in invariant subspaces. Operators for finite transformations and their relationship with generators. Lie algebras. Casimir operators. Discrete symmetry transformations. Scalar, pseudoscalar, vector and pseudo vector operators and selection rules. The temporal inversion. The Kramer degeneration of Kramer.

Theory of Collisions: cross sections and scattering amplitudes. Dispersion by a central potential, phase shifts partial wave decomposition. Unitarity. Potentials of finite range.

Symmetries in Quantum Mechanics: symmetry transformations and operators that represent symmetry transformations. Symmetry groups. Groups of continuous transformations: generators and the maximum set of operators that commute. The decomposition of the Hilbert space in invariant subspaces. Operators for finite transformations and their relationship with generators. Lie algebras. Casimir operators. Discrete symmetry transformations. Scalar, pseudoscalar, vector and pseudo vector operators and selection rules. The temporal inversion. The Kramer degeneration of Kramer.

Theory of Collisions: cross sections and scattering amplitudes. Dispersion by a central potential, phase shifts partial wave decomposition. Unitarity. Potentials of finite range.

Prerequisites

Quantum Mechanics I

Generic skills to reach

. Competence in oral and written communication;. Competence to solve problems;

. Competence in autonomous learning;

. Adaptability to new situations;

. Research skills;

. Competence for working in group;

. Critical thinking;

. Competence to communicate with people who are not experts in the field;

(by decreasing order of importance)

Teaching hours per semester

lectures | 45 |

theory-practical classes | 30 |

total of teaching hours | 75 |

Assessment

Sseminar or study visit | -- % |

Problem solving | 20 % |

Synthesis work thesis | -- % |

Project | -- % |

Research work | -- % |

Mini tests | 20 % |

Assessment Tests | -- % |

Exam | 60 % |

Bibliography of reference

B. H. Bransden, C. J. Joachain, Physics of Atoms and Molecules, Longman Group Limite, 1983

A. Z. Capri, Nonrelativistic Quantum Mechanics, Benjamin/Cummings Publishing Company, 1985

C. Cohen-Tannoudji, B. Diu, F. Laloë, Mécanique Quantique, Hermann, Paris, 1977

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (non-relativistic theory), Pergamn Press, 1997

A. Messiah, Quantum Mechanics, Dover Publications, N. Y., 1999

J. J. Sakurai, Moderm Quantum Mechanics, Addison-Wesley, 1993

A. Z. Capri, Nonrelativistic Quantum Mechanics, Benjamin/Cummings Publishing Company, 1985

C. Cohen-Tannoudji, B. Diu, F. Laloë, Mécanique Quantique, Hermann, Paris, 1977

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (non-relativistic theory), Pergamn Press, 1997

A. Messiah, Quantum Mechanics, Dover Publications, N. Y., 1999

J. J. Sakurai, Moderm Quantum Mechanics, Addison-Wesley, 1993

Teaching method

Presentation of the fundamental concepts, with appropriate background to this discipline. Classes of discussion / problem solving which seeks to connect the concepts covered to practical situations. Support to individual work of students for these to develop work on the collection and systematization of this information

Resources used