MATHEMATICAL METHODS IN QUANTUM MECHANICS

MATHEMATICAL METHODS IN QUANTUM MECHANICS

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iten
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

OVERVIEW

Language: Italian

AIMS AND CONTENT

LEARNING OUTCOMES

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 methods

Teaching style: In presence

SYLLABUS/CONTENT

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.

TEACHERS AND EXAM BOARD

Exam Board

PIERRE OLIVIER MARTINETTI (President)

CLAUDIO BARTOCCI (President)

NICOLA PINAMONTI (President)

MARCO BENINI

LESSONS

Teaching methods

Teaching style: In presence

LESSONS START

The class will start according to the academic calendar.

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

Vedi anche:

MATHEMATICAL METHODS IN QUANTUM MECHANICS

EXAMS

Exam description

Oral.