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##
MATHEMATICAL METHODS IN QUANTUM MECHANICS

## OVERVIEW

## AIMS AND CONTENT

### LEARNING OUTCOMES

### TEACHING METHODS

### SYLLABUS/CONTENT

## TEACHERS AND EXAM BOARD

### Exam Board

## LESSONS

### TEACHING METHODS

### LESSONS START

### Class schedule

## EXAMS

### EXAM DESCRIPTION

CODE | 90697 |
---|---|

ACADEMIC YEAR | 2019/2020 |

CREDITS | 5 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA |

SCIENTIFIC DISCIPLINARY SECTOR | MAT/07 |

LANGUAGE | Italian |

TEACHING LOCATION | GENOVA (Mathematics) |

SEMESTER | 2° Semester |

MODULES | This unit is a module of: |

TEACHING MATERIALS | AULAWEB |

Language: Italian

In this course will be presented the basic concepts of quantum mechanics, highlighting the mathematical techniques necessary for the strict formalization of this theory. In particular, the algebraic structure of quantum observables will be studied and the theorems necessary for the representation of this algebra will be analyzed. Finally, some instruments of operator theory and analysis of Hilbert spaces will be used to derive the evolution equations of Schrödinger and Heisenberg and to discuss their solutions.

Teaching style: In presence

TO BE UPDATED

**General relativity**

- Varietà differenziabili pseudo-riemanniane e campi vettoriali.
- Curvatura, trasporto parallelo e geodetiche.
- Equazioni di Einstein: loro soluzioni in casi particolari.

**Introduction to quantum theories**

- Basic concepts of quantum mechanics: measuremnts, observables, states.
- Observables algebra. GNS Theorem and formulation of quantum mechancis on Hilbert spaces.
- Automorphisms describing time evolution. Schrödinger and Heisenberg equations and properties of their generator. Theory of unbounded selfadjoint operators.

CLAUDIO BARTOCCI (President)

PIERRE OLIVIER MARTINETTI (President)

NICOLA PINAMONTI (President)

MARCO BENINI

Teaching style: In presence

The class will start according to the academic calendar.

Oral.