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University of Parma
Course catalogue
Università degli Studi di Parma
course catalogue

SUPPLEMENT TO MATHEMATICAL METHOD
cod. 18519

Academic year 2007/08
1° year of course - First semester
Professor
Academic discipline
Fisica teorica, modelli e metodi matematici (FIS/02)
Field
Discipline fisiche
Type of training activity
Basic
48 hours
of face-to-face activities
6 credits
hub:
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

Introduce the student to the basic concepts and to the methods of calculation of Quantum Mechanics

Prerequisites

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Course unit content

<br />Metric spaces, completeness, separability and completion. Vector, normed and Banach spaces, strong convergence. Unitary and Hilbert spaces, weak convergence, orthonormal systems and isomorphism with l_2 or C^n. Lebesgue integral, L_1 and L_2 spaces. Linear functionals, Riesz theorem, Dirac formalism. Limited linear operators, adjoint operator, isometric and unitary operators, projectors, invariant subspaces. Non-limited linear operators, operator graph, closed, symmetrical and self-adjoint operators. Spectral theory, resolving operator, operator spectrum. Decomposition and functions of operators, Stone theorem.  Application to Quantum Mechanics, position and moment operators, creation and destruction operators. Theory of distributions.

Full programme

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Bibliography

 Kolmogorov Fomin - Elementi di teoria delle funzioni e di analisi  funzionale, Ed. Mir 1980<br /> Bernardini Ragnisco Santini - Metodi matematici della fisica,<br />  La Nuova Italia 1994<br /> Abbati Cirelli - Metodi matematici per la fisica, Citta' Studi Ed. 1997<br /> Onofri - Teoria degli operatori lineari, Ed. Zara 1984<br /> Fano - Metodi matematici della meccanica quantistica, Zanichelli 1967<br /> 

Teaching methods

<br />Classroom lectures and exercices that are an integral part of them.<br />The examination includes a written test for admission to the subsequent oral test.

Assessment methods and criteria

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Other information

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