Complements of Mathematics for Chemists

Period of duration of course
Course info
Number of course hours
Number of hours of lecturers of reference
Number of hours of supplementary teaching

Type of exam

Oral exam


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The course is mostly directed to Master-level students in Chemistry.  A good knowledge of mathematical analysis and linear algebra is assumed. 


1) Banach and Hilbert Spaces

2) Geometry of Hilbert space. Orthonormal bases. 

3) Linear operators on Hilbert spaces. Bounded linear operators and functionals. Projectors.

4) Compact operators. Trace class operators.

5) Elements of spectral theory. Hilbert-Schmidt Theorem for compact self-adjoint operators.

6) Unbounded linear operators. Closed operators. 

7) Spectral Theorem for unbounded self-adjoint operators. One-parameter groups of unitary operators. Stone's Theorem.

8) Quantum-mechanical applications and examples.

Educational aims

The goal of the course is to provide students with the basic tools from Functional Analysis and Spectral Theory for the rigorous treatment of mathematical problems in quantum mechanics.

Bibliographical references

Sandro Graffi, Alcuni Aspetti Matematici della Meccanica Quantistica.  Quaderni dell'Istituto Nazionale di Alta Matematica, Gruppo Nazionale di Fisica Matematica, 2004.

Other references will be provided during the course of the lectures.