QUANTUM MECHANICS - MOD.1

The course is one of the compulsory educational activities of the Bachelor Degree in Engineering Physics and will allow the student to acquire the knowledge and the understanding of the fundamental and applied concepts of quantum mechanics.

The objective of the course is to provide broad knowledge of quantum mechanics, in particular in the study of one-dimensional potentials, the detailed study of the hydrogen atom, and in the understanding of the multi-electron atoms and of the periodic table. The last part of the course includes the study of the theory of perturbations.

At the end of the course (both modules), the students will be able to describe and calculate the most important quantum models, learn to use the language of the Dirac formalism, and to calculate transition probabilities between quantum states, using perturbation theory.

1. Knowledge and understanding
Knowing and understanding the laws of modern physics and their importance in the technological development
Understanding the scientific method and its relevance in the study of natural phenomena and in critical thinking
Understanding the importance of scientific culture in the innovation processes of modern technologies

2. Ability to apply knowledge and understanding
Using the necessary mathematics to describe natural phenomena
Applying the laws of quantum physics, in order to arrive at an understanding of the natural phenomena and to reach an organic view of the physical reality

3. Autonomy of judgment
Knowing how to evaluate the logical consistency of the results, both in for the case of theory and of experimental data.
Knowing how to recognize errors through a critical analysis of the applied method

4. Communication skills
Knowing how to communicate the knowledge learned using appropriate terminology, both in oral and written ways
Knowing how to interact with the teacher and with course colleagues in a respectful and constructive way, especially during group work

5. Learning skills
Knowing how to take notes, selecting and collecting information according to their importance and priority
Knowing how to be sufficiently autonomous in the collection of data and information relevant to the problem investigated

The course does not formally require having passed previous courses, but takes for granted many of the concepts covered in the courses of Calculus I and Calculus II (derivatives and integrals with one and more variables), Linear Algebra (spaces vectors and operations between vectors, eigenvalue equation), Mathematical Methods for Physics and Engineering (hamiltonian formalism, basics of Hilbert spaces), Physics I (motions of the point in one and more dimensions, conservation laws, angular momentum), Physics II (electrostatics, magnetostatics, wave equation), and Fundamentals of Telecommunications (Fourier transforms).

1. Schrödinger equation
Introduction to quantum physics with historical notes, Schrödinger equation and statistical interpretation
Momentum and Heisenberg's uncertainty principle
The time-independent Schrödinger equation

2. Quantum potentials in one dimension
The infinite quantum well
The free particle
The finite barrier of potential, the dispersion, the tunnel effect
The finished quantum well
The quantum harmonic oscillator

3. Quantum mechanics in three dimensions
The time-independent Schrödinger equation in 2D and 3D
The Schrödinger equation in 3D in polar spherical coordinates
The hydrogen atom

4. Formalism
Quantum mechanical formalism 1: linear algebra in n dimensions
Quantum mechanical formalism 2: the Dirac notation

Griffiths, Introduction to Quantum Mechanics, 3rd Edition, Cambridge University Press

The achievement of the learning goalsìs is assessed through participation in the activities of the group work, class exercises, a final written exam and an oral exam.

The final written exam consists of problems similar to those carried out in class during group work. The use of notes, books and other teaching material is not allowed during the final assignment. An example of the final assignment will be made available before the final exam.

Students attending the lessons can accumulate additional points by participating in the quizzes and exercises offered in class. The bonus will be added to the grade of the written assignment.

Seminars: limited frontal lecture, group work (peer-teaching, problem solving)
Exercise Sessions: group work (peer-teaching, problem solving)

Italian

written and oral

This subject deals with topics related to the macro-area "Human capital, health, education" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development