Quantum Chemistry
A.Y. 2025/2026
Learning objectives
Acquisition of the basic concepts of quantum theory (wave function, Schrodinger equation, quantization of energy levels, etc.) and their utilization in the description of atoms and molecules.
Expected learning outcomes
The student will be able to understand the physical meaning and the conditions of applicability of the laws and theorems at the base of Quantum Chemistry, applying them to the resolution of simple problems
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
1. Mathematical formulation of Quantum Mechanics - Operators and their properties. Dirac notation.
2. Postulates of Quantum Mechanics and measurement theory - The uncertainty principle. Quantum mechanics paradoxes: the Einstein-Podolsky-Rosen paradox and Schrödinger's cat.
3. The free particle and the construction of a wave packet.
4. Treatment of the harmonic oscillator using creation and annihilation operators.
5. General theory of angular momentum and angular momentum addition.
6. Spin angular momentum - Spin eigenfunctions for an N-electron system and their use in writing resonance structures. Measurement theory in the case of spin. The simplest example of an entangled state and its significance.
7. The hydrogen atom - Solving the Schrödinger equation for the simplest chemical system.
8. The variational principle and an introduction to perturbation methods.
9. Use of determinants to introduce antisymmetry - Calculation of matrix elements of the Hamiltonian operator for orthogonal orbitals and a brief mention of the non-orthogonal case.
10. The Hartree-Fock wavefunction - Derivation of the Hartree-Fock and Roothan equations.
11. Introduction to the electronic correlation problem and Density Functional Theory (DFT) - Their application in chemical modeling.
12. The density operator - Description of pure states and statistical mixtures. Possibility of describing a subsystem.
13. The formalism of second quantization.
2. Postulates of Quantum Mechanics and measurement theory - The uncertainty principle. Quantum mechanics paradoxes: the Einstein-Podolsky-Rosen paradox and Schrödinger's cat.
3. The free particle and the construction of a wave packet.
4. Treatment of the harmonic oscillator using creation and annihilation operators.
5. General theory of angular momentum and angular momentum addition.
6. Spin angular momentum - Spin eigenfunctions for an N-electron system and their use in writing resonance structures. Measurement theory in the case of spin. The simplest example of an entangled state and its significance.
7. The hydrogen atom - Solving the Schrödinger equation for the simplest chemical system.
8. The variational principle and an introduction to perturbation methods.
9. Use of determinants to introduce antisymmetry - Calculation of matrix elements of the Hamiltonian operator for orthogonal orbitals and a brief mention of the non-orthogonal case.
10. The Hartree-Fock wavefunction - Derivation of the Hartree-Fock and Roothan equations.
11. Introduction to the electronic correlation problem and Density Functional Theory (DFT) - Their application in chemical modeling.
12. The density operator - Description of pure states and statistical mixtures. Possibility of describing a subsystem.
13. The formalism of second quantization.
Prerequisites for admission
Basic knowledge of math, physics and chemical physics acquired during the first years of bachelor courses either in chemistry for the course Instituzioni di matematica, Fisica generale and Chimica Fisica della materia e fondamenti di spettroscopia or Istituzioni di Matematica, Fisica generale and Chimica Fisica I and II for the degree in Chimica industriale e gestionale.
Teaching methods
The course will be taught either using the blackboard or electronic slides. The course will be taught in Italian. The student is warmly advised to attend the lessons. 6 CFU: 48 hours of teaching.
Teaching Resources
Materiale didattico messo a disposizione del Docente
A.Szabo; Modern Quantum Chemistry - Dover
Cohen-Tannoudji; Quantum Mechanics, vol. 1 - Wiley
A.Szabo; Modern Quantum Chemistry - Dover
Cohen-Tannoudji; Quantum Mechanics, vol. 1 - Wiley
Assessment methods and Criteria
The exam consists of a written test, with a possible clarification interview on the written test. The student is required to have understood the physical meaning and the demonstrations discussed in class.
The written test will be evaluated based on the correctness of the paper, the clarity of the exposition and the rigor of the exposition
The written test will be evaluated based on the correctness of the paper, the clarity of the exposition and the rigor of the exposition
Professor(s)