Physics | University of Parma

Professor
Academic discipline: Fisica teorica, modelli e metodi matematici (FIS/02)
Field: Teorico e dei fondamenti della fisica
Type of training activity: Characterising

48 hours
of face-to-face activities

6 credits

hub:

course unit
in - - -

lectures timetable unavailable

exam calls

Learning objectives

An introduction to methods and concepts of operator theory for quantum physics
and mathematical physics

Prerequisites

First level courses in analysis and geometry

Course unit content

Linear operators in finite dimensional spaces, concepts and methods

Full programme

Numerical fields, recalls
Linear Manifold, linear dependance and independence, dimension
Abstract vectorial spaces
Real and complex spaces, isomorphism
Scalar product, orthogonality
Metrics spaces. Topological notions.
Bases, orthogonal systems, orthogonalization.
Chanhes of bases.
Linear functionals and Riesz Theorem
Dirac’s formalis
Vectorial sequences and convergence
Linear application and matrices
Notion of abstract linear operator
Rapresentation of operators.
Diagonalization
Adjoint operators.
Eigenvalues and eigenvectors.
Hermitiam, unitary, normal operators.
Complete systems of hermitian operators.
Projectors.
Resolvent and spectrum.
Functions of operators.
Some inequalities.
Polynomials and orthogonal functions.
Approximation of functions.
Recalls about the Fourier Series.
Hints on infinite dimensional spaces.
Completeness.

Bibliography

E. Onofri: Lezioni sulla Teoria degli Operatori Lineari, Zara, Parma
- C. Bernardini, O. Ragnisco, P.M. Santini: Metodi Matematici della Fisica, Nuova Italia Scientifica Roma 1993
- F.G. Tricomi: Istituzioni di Analisi Superiore, Cedam, Padova
- G. Fano: Metodi Matematici della Meccanica Quantistica, Zanichelli, Bologna
- M. R. Spiegel: Variabili Complesse, Etas, collana Schaum
- A. Kolmogorov e S Fomin : Analisi Funzionale, Mir
- W.Rudin: Real and Complex Analysis, Mc Graw Hill

Teaching methods

Frontal lessons and exercises.

Assessment methods and criteria

Written and oral examination

Other information

- - -

MATHEMATICAL METHODS FOR PHYSICS cod. 00709