## Learning objectives

Knowledge and understanding: the students will acquire basic knowledge in quantum mechanics and specific knowledge on applications of quantum mechanics to chemically relevant problems.

Applying knowledge and understanding: the students will acquire the tools required to re-interpret and formally describe chemical knowledge acquired in basic chemical courses (wavefunction, orbitals, chemical bond, spin, etc...) to reinforce a coherent and robust frame of knowledge in chemical sciences..

Learning skills: the student will acquire methodological competences and the basic tools of chemical quantum mechanics as to be able to read and understand specialistic literature.

Communication skills: Mastering of the specialistic language as to allow the student to interact with experts in the chemical-physical field and to effectively transfer knowledge also to non-specialized audience.

## Prerequisites

To fruitfully access the course students must master basic mathematical tools, and have a good knowledge of basic concepts in physics.

## Course unit content

Quantum Mechanics: an introduction

A few exact solutions of the Schrödinger equation

Methods of approximation

Symmetry in Quantum Mechanics

Atoms and molecules: some basic concepts

Atomic structure

Molecular structure

## Full programme

Introduction to quantum mechanics

*the double-slit experiment, photon polarization and teh superposition principle

*states & operators, vectors & matrices

*observables, eigenstates and measurements

*commutability & compatibility

*Schrödinger representation

*Schrödinger equation

Exact solutions of the Schrödinger equation

*the free particle

*the particle in a box

*the harmonic oscillator

*the rigid rotor, angula momenta & spin

*one-electron atoms

Approximation methods

*perturbation theory for stationary states

*variational method

Symmetry in quantum mechanics

*symmetry & group theory

*symmetry & quantum mechanics

*point groups, continuous groups

*exchange symmetry: fermions & bosons

Atoms & molecules: some basic concepts

*the adiabatic approximation (Born-Oppenheimer)

*mean-field approximation, atomic/molecular orbitals

Atomic structure

*configurations & aufbau

*coupling of angular momenta

*spin-orbit coupling

Molecolar structure

*chemical bond: the hydrogen molecule

*diatomic homonuclear molecules

*polyatomic molecules

*hybrid orbitals

*transition metal complexes

*electronic structure calculations (primer)

*the Huckel method

*vibrations of polyatomic molecules

## Bibliography

The reference manual is:

P.W. Atkins and R.S. Friedman, Molecular Quantum Mechanics, Oxford University Press, 2011 - V edition

complemented with lecture notes available to the students.

## Teaching methods

The course, integrated with a laboratory course, develops in 40 hours of frontal teaching where basic concepts will be introduced, and in 15 hours of guided exercise, to apply acquired knowledge to specific problems.

## Assessment methods and criteria

The exam, integrated with the corresponding Laboratory, verifies (a) the mastering of basic concepts of quantum mechanics and their application to chemical problems; (b) the ability of the student to present relevant concepts in a clear and precise way, properly using technical-scientific language, (c) the capacity to face chemica problems using formal tools of quantum mechanics;(d) the capacity to extract information from the analysis of data.

The oral examination is preceded by a simple written test to evaluate if the student knows the basic necessary skills. The student admitted to the oral proof will be asked to describe one of the laboratory experiment. Then two more questions will be asked on topics of the theoretical course. The successful students masters the topic in the programs of both courses in terms of knowledge and in of ability to reliably and properly communicate using the scientific technical language.

The unsuccessful student cannot access the exam before two weeks from failure. The rare students unsuccessul for more than 4 times, are asked to access the exam no more than once per session.

## Other information

lecture notes are available to the students.

The teacher is available to the student upon request to discuss and clarify specific issues.