QUANTUM CHEMISTRY

This course is one of the core educational activities in the Master's degree in Sustainable Chemistry and Technology,
that describes some of the common approaches of quantum mechanics to the fundamental
understanding of chemical systems. The microscopic (or molecular) perspective
builds on atomic and molecular models to predict
macroscopically observable properties will be studied. In particular, we will discuss two main
themes during this course including quantum mechanics and spectroscopy.
Learning objectives involve developing an understanding
of quantum mechanical principles, and applying these principles to master the
underlying concepts of electronic structure for atoms, molecules and nanostructures.

The student active participation and attendance at classes (theoretical lessons and practical activities) together with independent study, will allow to reach the following abilities of learning and comprehension:
1. to learn the main mathematical methods used in quantum mechanics;
2. To learn the standard methods to study molecular and nano-structured systems;
Linking material learned in
class to modern physical chemistry techniques and research will be highlighted to
give you opportunities to see how Physical Chemists are solving current, real-world problems.

This is a math-intensive course, and it is expected that students have previous
experience with calculus. In addition, students should be familiar with the concepts learned in calculus-based physics. We will review some mathematical principles along the way
so that students can focus on learning the physical chemistry material.

1 The Wave Function

The Schrödinger Equation
The Statistical Interpretation
Probability
Discrete Variables
Continuous Variables
Normalization
Momentum
The Uncertainty Principle

2 Time-Independent Schrödinger Equation

Stationary States
The Infinite Square Well
The Harmonic Oscillator:
Algebraic Method
Analytic Method
The Free Particle
The Delta-Function Potential
Bound States and Scattering States
The Delta-Function Well
The Finite Square Well

3 Formalism

Hilbert Space
Observables
Hermitian Operators
Determinate States
Eigenfunctions of a Hermitian Operator
Discrete Spectra
Continuous Spectra
Generalized Statistical Interpretation
Vectors and Operators
Bases in Hilbert Space
Dirac Notation

4 Quantum Mechanics in Three Dimensions

The Schrödinger Equation
Spherical Coordinates
The Angular Equation
The Radial Equation
The Hydrogen Atom
The Radial Wave Function
The Spectrum of Hydrogen
Angular Momentum
Eigenvalues
Eigenfunctions
Spin
Spin 1/2

D. Griffith, Introduction to Quantum Mechanics, Cambridge University Press.
C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics Volume 1, 2nd edition (2019), Wiley-VCH.
R. Shankar, Principles of Quantum Mechanics, Second edition, Springer
R. Eisberg, R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles Second Edition, John Wiley & Sons.
L. Pauling,E. Bright Wilson, Introduction to Quantum Mechanics with Applications to Chemistry, Dover Edition.
W. Ashcroft Neil, D. Mermin, Solid State Physics, Thomson Press.
G. B. Arfken and H.Weber Mathematical Methods for Physicists (Elsevier 2005)
M. Boas Mathematical Methods for the Physical Sciences, 3rd edition, John Wiley and Sons

Problem Sets
There is no better way to master Physical Chemistry than by solving problems. The
essence of this subject demands connecting abstract mathematical ideas with the
experimentally observed behaviour of chemical systems. Therefore, eight (8)
problem sets will be posted on Blackboard due in class on the specified date.
Working together in study groups of 3-4 students is
encouraged as a helpful and enjoyable way to overcome conceptual obstacles and
share the satisfaction of gained understanding. In reality, at the heart of good
science is collaboration, so work together with your colleagues to solve problems.
Midterm Exams (85%)
There will be two (2) in-class midterm exams given during the semester,
worth 85% of the course point total. A comprehensive, final exam will be given during the examination session worth 25% (oral exam).

For those students who will not give Midterm exams, a comprehensive final exam will be given during the examination session (written+oral exams).

face to face lessons (using Blackboard )

English

Accessibility, Disability and Inclusion

Accommodation and support services for students with disabilities and students with specific learning impairments:
Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding supportservices and accommodation available to students with disabilities. This includes students with mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). In the case of disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.

THE STRUCTURE AND CONTENT OF THE COURSE MAY CHANGE AS A RESULT OF THE COVID-19 EPIDEMIC

written and oral

This subject deals with topics related to the macro-area "Climate change and energy" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development